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oeis

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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A000101
Record gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps).
[ "3", "5", "11", "29", "97", "127", "541", "907", "1151", "1361", "9587", "15727", "19661", "31469", "156007", "360749", "370373", "492227", "1349651", "1357333", "2010881", "4652507", "17051887", "20831533", "47326913", "122164969", "189695893", "191913031", "387096383", "436273291", "1294268779" ]
[ "nonn", "nice" ]
160
1
1
[ "A000040", "A000101", "A001223", "A002386", "A005250", "A005669", "A107578", "A111943" ]
[ "M2485", "N0984" ]
N. J. A. Sloane
2025-02-16T08:32:19
oeisdata/seq/A000/A000101.seq
2aa1e3b0460963ad027c98f9ff22fa9c
A000102
a(n) = number of compositions of n in which the maximum part size is 4.
[ "0", "0", "0", "0", "1", "2", "5", "12", "27", "59", "127", "269", "563", "1167", "2400", "4903", "9960", "20135", "40534", "81300", "162538", "324020", "644282", "1278152", "2530407", "5000178", "9863763", "19427976", "38211861", "75059535", "147263905", "288609341", "565047233", "1105229439", "2159947998" ]
[ "nonn", "nice", "easy", "changed" ]
64
0
6
null
[ "M1409", "N0551" ]
N. J. A. Sloane
2025-04-24T17:22:43
oeisdata/seq/A000/A000102.seq
fd7fdf503cdbb1c798be1cc647e8ea80
A000103
Number of n-node triangulations of sphere in which every node has degree >= 4.
[ "0", "0", "1", "1", "2", "5", "12", "34", "130", "525", "2472", "12400", "65619", "357504", "1992985", "11284042", "64719885", "375126827", "2194439398", "12941995397", "76890024027", "459873914230", "2767364341936", "16747182732792" ]
[ "nonn", "hard", "more" ]
51
4
5
[ "A000103", "A000109", "A081621" ]
[ "M1423", "N0559" ]
N. J. A. Sloane
2025-02-16T08:32:19
oeisdata/seq/A000/A000103.seq
c5563f063126fc6723899c2e795500dc
A000104
Number of n-celled free polyominoes without holes.
[ "1", "1", "1", "2", "5", "12", "35", "107", "363", "1248", "4460", "16094", "58937", "217117", "805475", "3001127", "11230003", "42161529", "158781106", "599563893", "2269506062", "8609442688", "32725637373", "124621833354", "475368834568", "1816103345752", "6948228104703", "26618671505989", "102102788362303" ]
[ "nonn", "nice", "hard" ]
75
0
4
[ "A000104", "A000105", "A006724", "A006746", "A006747", "A006748", "A006749", "A018190", "A054361", "A056877", "A056878", "A056879", "A056880", "A056881", "A056882", "A070765", "A266549", "A308300", "A357647", "A357648" ]
[ "M1424", "N0560" ]
N. J. A. Sloane
2024-03-21T21:03:41
oeisdata/seq/A000/A000104.seq
35906601790d916275acdda04dfea3ec
A000105
Number of free polyominoes (or square animals) with n cells.
[ "1", "1", "1", "2", "5", "12", "35", "108", "369", "1285", "4655", "17073", "63600", "238591", "901971", "3426576", "13079255", "50107909", "192622052", "742624232", "2870671950", "11123060678", "43191857688", "168047007728", "654999700403", "2557227044764", "9999088822075", "39153010938487", "153511100594603" ]
[ "nonn", "hard", "nice", "core" ]
250
0
4
[ "A000104", "A000105", "A000228", "A000577", "A000988", "A001168", "A001419", "A006746", "A006747", "A006748", "A006749", "A006765", "A030228", "A054359", "A054360", "A056877", "A056878", "A103465", "A142886", "A144553", "A144554", "A210996", "A366766" ]
[ "M1425", "N0561" ]
N. J. A. Sloane
2025-03-14T21:16:24
oeisdata/seq/A000/A000105.seq
73da3d342057890ac49016e5d12f7388
A000106
2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees.
[ "1", "2", "5", "12", "30", "74", "188", "478", "1235", "3214", "8450", "22370", "59676", "160140", "432237", "1172436", "3194870", "8741442", "24007045", "66154654", "182864692", "506909562", "1408854940", "3925075510", "10959698606", "30665337738", "85967279447", "241433975446", "679192039401", "1913681367936", "5399924120339" ]
[ "nonn", "nice", "easy" ]
65
2
2
[ "A000081", "A000106", "A000242", "A000300", "A000343", "A000395", "A027852", "A335362", "A339067" ]
[ "M1415", "N0553" ]
N. J. A. Sloane
2023-11-03T16:18:54
oeisdata/seq/A000/A000106.seq
a3151b9377174727560aabb6a04867bd
A000107
Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates.
[ "0", "1", "2", "5", "13", "35", "95", "262", "727", "2033", "5714", "16136", "45733", "130046", "370803", "1059838", "3035591", "8710736", "25036934", "72069134", "207727501", "599461094", "1731818878", "5008149658", "14496034714", "41993925955", "121747732406", "353221737526", "1025471857282", "2978995353959", "8658997820084" ]
[ "nonn", "easy", "nice" ]
69
0
3
[ "A000081", "A000107", "A008295", "A339067" ]
[ "M1442", "N0570" ]
N. J. A. Sloane
2023-03-23T23:09:14
oeisdata/seq/A000/A000107.seq
4283059fefdf70af1ff4fbd6cb77728d
A000108
Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
[ "1", "1", "2", "5", "14", "42", "132", "429", "1430", "4862", "16796", "58786", "208012", "742900", "2674440", "9694845", "35357670", "129644790", "477638700", "1767263190", "6564120420", "24466267020", "91482563640", "343059613650", "1289904147324", "4861946401452", "18367353072152", "69533550916004", "263747951750360", "1002242216651368", "3814986502092304" ]
[ "core", "nonn", "easy", "eigen", "nice" ]
2,100
0
3
[ "A000081", "A000108", "A000142", "A000207", "A000245", "A000344", "A000588", "A000736", "A000753", "A000957", "A000984", "A001003", "A001147", "A001190", "A001392", "A001453", "A001477", "A001683", "A001699", "A001764", "A001791", "A001795", "A002057", "A002390", "A002420", "A003046", "A003517", "A003518", "A003519", "A006480", "A006858", "A008276", "A008549", "A009766", "A014137", "A014138", "A014140", "A014486", "A022553", "A024492", "A030237", "A032357", "A032443", "A033184", "A033552", "A038003", "A039599", "A046161", "A047072", "A048990", "A051168", "A059288", "A059365", "A060854", "A068875", "A069640", "A078920", "A086117", "A088327", "A091962", "A094216", "A094638", "A094639", "A098597", "A099039", "A099731", "A106566", "A119822", "A119861", "A119908", "A120274", "A120275", "A120303", "A120304", "A121839", "A123352", "A124926", "A129763", "A130020", "A137697", "A154559", "A161581", "A163960", "A167892", "A167893", "A176137", "A179277", "A208355", "A211611", "A259667", "A264663", "A268813", "A275431", "A332602", "A368025", "A369314" ]
[ "M1459", "N0577" ]
N. J. A. Sloane
2025-02-08T10:25:23
oeisdata/seq/A000/A000108.seq
1f93724741d3d8a94311db1a3f1c1fd7
A000109
Number of simplicial polyhedra with n vertices; simple planar graphs with n vertices and 3n-6 edges; maximal simple planar graphs with n vertices; planar triangulations with n vertices; triangulations of the sphere with n vertices; 3-connected cubic planar graphs on 2n-4 vertices.
[ "1", "1", "1", "2", "5", "14", "50", "233", "1249", "7595", "49566", "339722", "2406841", "17490241", "129664753", "977526957", "7475907149", "57896349553", "453382272049", "3585853662949", "28615703421545" ]
[ "nonn", "nice", "hard", "more", "core" ]
130
3
4
[ "A000109", "A000944", "A005964", "A007021", "A007816", "A058378", "A111358", "A253882" ]
[ "M1469", "N0580" ]
N. J. A. Sloane
2025-02-16T08:32:19
oeisdata/seq/A000/A000109.seq
2c6560825ef27bb7b4c2092396b820c7
A000110
Bell or exponential numbers: number of ways to partition a set of n labeled elements.
[ "1", "1", "2", "5", "15", "52", "203", "877", "4140", "21147", "115975", "678570", "4213597", "27644437", "190899322", "1382958545", "10480142147", "82864869804", "682076806159", "5832742205057", "51724158235372", "474869816156751", "4506715738447323", "44152005855084346", "445958869294805289", "4638590332229999353", "49631246523618756274" ]
[ "core", "nonn", "easy", "nice" ]
1,378
0
3
[ "A000045", "A000108", "A000110", "A000166", "A000204", "A000255", "A000296", "A000311", "A000371", "A000798", "A001035", "A001861", "A001927", "A001929", "A003422", "A003465", "A005001", "A006056", "A006057", "A006058", "A006059", "A008277", "A011971", "A024716", "A027710", "A029761", "A048993", "A049020", "A054767", "A058692", "A060719", "A061462", "A078944", "A084423", "A085686", "A087650", "A094262", "A102661", "A103293", "A121207", "A123158", "A144180", "A144223", "A144263", "A144293", "A152432", "A165194", "A165196", "A173110", "A182386", "A186021", "A212431", "A221159", "A227840", "A243991" ]
[ "M1484", "N0585" ]
N. J. A. Sloane
2025-04-13T16:28:17
oeisdata/seq/A000/A000110.seq
6c39e2e0e6056814aca08ad96074d75b
A000111
Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250).
[ "1", "1", "1", "2", "5", "16", "61", "272", "1385", "7936", "50521", "353792", "2702765", "22368256", "199360981", "1903757312", "19391512145", "209865342976", "2404879675441", "29088885112832", "370371188237525", "4951498053124096", "69348874393137901", "1015423886506852352", "15514534163557086905", "246921480190207983616", "4087072509293123892361" ]
[ "nonn", "core", "eigen", "nice", "easy" ]
746
0
4
[ "A000111", "A000182", "A000258", "A000311", "A000364", "A002105", "A002846", "A005121", "A008280", "A008281", "A008282", "A008970", "A010094", "A059720", "A109449", "A177762", "A181937", "A186365", "A229892", "A250261", "A258829", "A262124", "A275784", "A292050", "A301344", "A318813", "A320270", "A330474", "A330665", "A330679", "A340315", "A349264" ]
[ "M1492", "N0587" ]
N. J. A. Sloane
2025-03-10T11:12:52
oeisdata/seq/A000/A000111.seq
9a1ba385d34186b76810fe377fd04d5d
A000112
Number of partially ordered sets ("posets") with n unlabeled elements.
[ "1", "1", "2", "5", "16", "63", "318", "2045", "16999", "183231", "2567284", "46749427", "1104891746", "33823827452", "1338193159771", "68275077901156", "4483130665195087" ]
[ "nonn", "hard", "more", "core", "nice" ]
188
0
3
[ "A000112", "A000608", "A000798", "A001035", "A001930", "A006057", "A065066", "A079263", "A079265", "A263859", "A316978", "A319559", "A326939", "A326943", "A326944", "A326947", "A342447" ]
[ "M1495", "N0588" ]
N. J. A. Sloane
2024-07-07T13:45:47
oeisdata/seq/A000/A000112.seq
e5dffbfa3c22c90258eb57573484abc2
A000113
Number of transformation groups of order n.
[ "1", "3", "4", "3", "6", "12", "8", "6", "4", "18", "12", "12", "14", "24", "24", "6", "18", "12", "20", "18", "32", "36", "24", "24", "30", "42", "12", "24", "30", "72", "32", "12", "48", "54", "48", "12", "38", "60", "56", "36", "42", "96", "44", "36", "24", "72", "48", "24", "56", "90", "72", "42", "54", "36", "72", "48", "80", "90", "60", "72", "62", "96", "32", "12", "84", "144", "68" ]
[ "nonn", "easy", "mult" ]
26
1
2
[ "A000113", "A001615" ]
null
N. J. A. Sloane
2022-10-23T02:54:44
oeisdata/seq/A000/A000113.seq
4f6927d4811708c96d44cbef75f9fe55
A000114
Number of cusps of principal congruence subgroup GAMMA^{hat}(n).
[ "3", "4", "6", "12", "12", "24", "24", "36", "36", "60", "48", "84", "72", "96", "96", "144", "108", "180", "144", "192", "180", "264", "192", "300", "252", "324", "288", "420", "288", "480", "384", "480", "432", "576", "432", "684", "540", "672", "576", "840", "576", "924", "720", "864", "792", "1104", "768", "1176", "900", "1152", "1008", "1404", "972", "1440" ]
[ "nonn", "easy" ]
25
2
1
[ "A000114", "A001766" ]
null
N. J. A. Sloane
2019-10-23T15:53:31
oeisdata/seq/A000/A000114.seq
63fba952cc7fe79c8c1bfe01b834a398
A000115
Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).
[ "1", "1", "2", "2", "3", "4", "5", "6", "7", "8", "10", "11", "13", "14", "16", "18", "20", "22", "24", "26", "29", "31", "34", "36", "39", "42", "45", "48", "51", "54", "58", "61", "65", "68", "72", "76", "80", "84", "88", "92", "97", "101", "106", "110", "115", "120", "125", "130", "135", "140", "146", "151", "157", "162", "168", "174", "180", "186", "192", "198", "205", "211", "218", "224", "231", "238" ]
[ "nonn", "easy" ]
57
0
3
[ "A000115", "A001304", "A008616", "A008720" ]
[ "M0279", "N0098" ]
N. J. A. Sloane
2022-09-08T08:44:27
oeisdata/seq/A000/A000115.seq
3917ffdf2b688439f44357da8092d84e
A000116
Number of even sequences with period 2n (bisection of A000013).
[ "1", "2", "4", "8", "20", "56", "180", "596", "2068", "7316", "26272", "95420", "349716", "1290872", "4794088", "17896832", "67110932", "252648992", "954444608", "3616828364", "13743921632", "52357746896", "199911300472", "764877836468", "2932031358484", "11258999739560", "43303843861744", "166799988689300" ]
[ "nonn", "easy", "nice" ]
47
0
2
[ "A000013", "A000116", "A026119" ]
[ "M1156", "N0440" ]
N. J. A. Sloane
2024-03-14T05:20:00
oeisdata/seq/A000/A000116.seq
5a1712e56f4e9fa3cbf62776a44c7a75
A000117
Number of even sequences with period 2n (bisection of A000011).
[ "1", "2", "4", "8", "18", "44", "122", "362", "1162", "3914", "13648", "48734", "176906", "649532", "2405236", "8964800", "33588234", "126390032", "477353376", "1808676326", "6872485104", "26179922024", "99957747388", "382443112538", "1466024067850", "5629516646996", "21651955485304", "83400061453514" ]
[ "nonn", "easy", "nice" ]
33
0
2
[ "A000011", "A000117" ]
[ "M1150", "N0438" ]
N. J. A. Sloane
2022-06-26T04:14:55
oeisdata/seq/A000/A000117.seq
45d688d9597003931d18550af76b34a1
A000118
Number of ways of writing n as a sum of 4 squares; also theta series of four-dimensional cubic lattice Z^4.
[ "1", "8", "24", "32", "24", "48", "96", "64", "24", "104", "144", "96", "96", "112", "192", "192", "24", "144", "312", "160", "144", "256", "288", "192", "96", "248", "336", "320", "192", "240", "576", "256", "24", "384", "432", "384", "312", "304", "480", "448", "144", "336", "768", "352", "288", "624", "576", "384", "96", "456", "744", "576", "336", "432", "960", "576", "192" ]
[ "nonn", "easy", "nice" ]
195
0
2
[ "A000118", "A000122", "A000203", "A000265", "A004011", "A005879", "A046897", "A096727", "A122141", "A236923", "A236926", "A236927", "A236928", "A236930", "A236931", "A236932", "A236933", "A286815", "A319574" ]
null
N. J. A. Sloane
2024-10-14T12:17:28
oeisdata/seq/A000/A000118.seq
f02ceff459096cdb28ee86dfbf4469ef
A000119
Number of representations of n as a sum of distinct Fibonacci numbers.
[ "1", "1", "1", "2", "1", "2", "2", "1", "3", "2", "2", "3", "1", "3", "3", "2", "4", "2", "3", "3", "1", "4", "3", "3", "5", "2", "4", "4", "2", "5", "3", "3", "4", "1", "4", "4", "3", "6", "3", "5", "5", "2", "6", "4", "4", "6", "2", "5", "5", "3", "6", "3", "4", "4", "1", "5", "4", "4", "7", "3", "6", "6", "3", "8", "5", "5", "7", "2", "6", "6", "4", "8", "4", "6", "6", "2", "7", "5", "5", "8", "3", "6", "6", "3", "7", "4", "4", "5", "1", "5", "5", "4", "8", "4", "7", "7", "3", "9", "6", "6", "9", "3", "8", "8", "5" ]
[ "nonn", "nice", "look" ]
143
0
4
[ "A000119", "A000121", "A003107", "A007000", "A013583", "A080097", "A096748" ]
[ "M0101", "N0037" ]
N. J. A. Sloane
2025-03-26T11:28:29
oeisdata/seq/A000/A000119.seq
790be2e2145c8c3371898904c5ed7540
A000120
1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).
[ "0", "1", "1", "2", "1", "2", "2", "3", "1", "2", "2", "3", "2", "3", "3", "4", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "3", "4", "4", "5", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "3", "4", "4", "5", "2", "3", "3", "4", "3", "4", "4", "5", "3", "4", "4", "5", "4", "5", "5", "6", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "3", "4", "4", "5", "2", "3", "3", "4", "3", "4", "4", "5", "3", "4", "4", "5", "4", "5", "5", "6", "2", "3", "3", "4", "3", "4", "4", "5", "3" ]
[ "nonn", "easy", "core", "nice", "hear", "look", "base" ]
477
0
4
[ "A000069", "A000120", "A000788", "A001620", "A001792", "A001969", "A007088", "A007814", "A007953", "A010062", "A011371", "A023416", "A053735", "A053737", "A053824", "A053827", "A053828", "A053829", "A053830", "A053831", "A053832", "A053833", "A053834", "A053835", "A053836", "A055640", "A055641", "A059015", "A063787", "A070939", "A080791", "A102669", "A102685", "A117804", "A122840", "A122841", "A131534", "A135416", "A160093", "A160094", "A196563", "A196564", "A230952", "A344716" ]
[ "M0105", "N0041" ]
N. J. A. Sloane
2025-04-03T09:42:03
oeisdata/seq/A000/A000120.seq
9ffc7bafde07f3c14e450fcf7f4ebbed
A000121
Number of representations of n as a sum of Fibonacci numbers (1 is allowed twice as a part).
[ "1", "2", "2", "3", "3", "3", "4", "3", "4", "5", "4", "5", "4", "4", "6", "5", "6", "6", "5", "6", "4", "5", "7", "6", "8", "7", "6", "8", "6", "7", "8", "6", "7", "5", "5", "8", "7", "9", "9", "8", "10", "7", "8", "10", "8", "10", "8", "7", "10", "8", "9", "9", "7", "8", "5", "6", "9", "8", "11", "10", "9", "12", "9", "11", "13", "10", "12", "9", "8", "12", "10", "12", "12", "10", "12", "8", "9", "12", "10", "13", "11", "9", "12", "9", "10", "11", "8", "9", "6", "6", "10", "9" ]
[ "nonn" ]
44
0
2
[ "A000119", "A000121", "A083853", "A274262", "A356874" ]
[ "M0249", "N0088" ]
N. J. A. Sloane
2025-01-05T19:51:30
oeisdata/seq/A000/A000121.seq
511fc3fac325fe678dc93b2c6f7b3eea
A000122
Expansion of Jacobi theta function theta_3(x) = Sum_{m =-oo..oo} x^(m^2) (number of integer solutions to k^2 = n).
[ "1", "2", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0" ]
[ "nonn", "easy", "nice" ]
155
0
2
[ "A000007", "A000122", "A001650", "A002448", "A004015", "A004016", "A008444", "A008445", "A008446", "A008447", "A008448", "A008449", "A010052", "A010054", "A089801", "A122141", "A286815" ]
null
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000122.seq
91d26fdefd2fc64f3723eb39d7d7e214
A000123
Number of binary partitions: number of partitions of 2n into powers of 2.
[ "1", "2", "4", "6", "10", "14", "20", "26", "36", "46", "60", "74", "94", "114", "140", "166", "202", "238", "284", "330", "390", "450", "524", "598", "692", "786", "900", "1014", "1154", "1294", "1460", "1626", "1828", "2030", "2268", "2506", "2790", "3074", "3404", "3734", "4124", "4514", "4964", "5414", "5938", "6462", "7060", "7658", "8350", "9042", "9828" ]
[ "nonn", "easy", "core", "nice" ]
262
0
2
[ "A000041", "A000123", "A002033", "A002487", "A002577", "A005704", "A005706", "A018819", "A023359", "A033485", "A040039", "A072170", "A089177", "A100529", "A145515", "A171370" ]
[ "M1011", "N0378" ]
N. J. A. Sloane
2025-01-05T19:51:30
oeisdata/seq/A000/A000123.seq
070140cfff169379253713cfe5a96bb6
A000124
Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.
[ "1", "2", "4", "7", "11", "16", "22", "29", "37", "46", "56", "67", "79", "92", "106", "121", "137", "154", "172", "191", "211", "232", "254", "277", "301", "326", "352", "379", "407", "436", "466", "497", "529", "562", "596", "631", "667", "704", "742", "781", "821", "862", "904", "947", "991", "1036", "1082", "1129", "1177", "1226", "1276", "1327", "1379" ]
[ "nonn", "core", "easy", "nice" ]
671
0
2
[ "A000096", "A000124", "A000125", "A000127", "A000217", "A002061", "A002522", "A002620", "A003600", "A005408", "A006261", "A014206", "A016028", "A016813", "A025732", "A025739", "A033547", "A051601", "A055469", "A055503", "A058331", "A072863", "A080856", "A086514", "A144328", "A161701", "A161702", "A161703", "A161704", "A161706", "A161707", "A161708", "A161710", "A161711", "A161712", "A161713", "A161715", "A177862", "A228918", "A263883" ]
[ "M1041", "N0391" ]
N. J. A. Sloane
2025-03-09T05:05:59
oeisdata/seq/A000/A000124.seq
fe5bb87833591cda58b3e4395b7c670a
A000125
Cake numbers: maximal number of pieces resulting from n planar cuts through a cube (or cake): C(n+1,3) + n + 1.
[ "1", "2", "4", "8", "15", "26", "42", "64", "93", "130", "176", "232", "299", "378", "470", "576", "697", "834", "988", "1160", "1351", "1562", "1794", "2048", "2325", "2626", "2952", "3304", "3683", "4090", "4526", "4992", "5489", "6018", "6580", "7176", "7807", "8474", "9178", "9920", "10701", "11522", "12384", "13288", "14235", "15226" ]
[ "nonn", "easy", "nice" ]
288
0
2
[ "A000027", "A000124", "A000125", "A000127", "A002522", "A002620", "A003600", "A005408", "A006261", "A016813", "A047694", "A051601", "A058331", "A063865", "A077028", "A077043", "A080856", "A086514", "A100503", "A100504", "A123596", "A134396", "A152947", "A161701", "A161705", "A161706", "A161708", "A161710", "A161713", "A161715", "A283551" ]
[ "M1100", "N0419" ]
N. J. A. Sloane
2025-03-08T15:13:32
oeisdata/seq/A000/A000125.seq
f02d61714f32ac58822dcaf7221c589a
A000126
A nonlinear binomial sum.
[ "1", "2", "4", "8", "15", "27", "47", "80", "134", "222", "365", "597", "973", "1582", "2568", "4164", "6747", "10927", "17691", "28636", "46346", "75002", "121369", "196393", "317785", "514202", "832012", "1346240", "2178279", "3524547", "5702855", "9227432", "14930318", "24157782", "39088133", "63245949" ]
[ "nonn", "easy" ]
171
1
2
[ "A000045", "A000071", "A000126", "A001924", "A005251", "A007931", "A065220", "A066067", "A066982", "A122554", "A169985" ]
[ "M1103", "N0421" ]
N. J. A. Sloane
2025-01-05T19:51:30
oeisdata/seq/A000/A000126.seq
54f4ebed949c767544f8ab3eaa1bafc6
A000127
Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes.
[ "1", "2", "4", "8", "16", "31", "57", "99", "163", "256", "386", "562", "794", "1093", "1471", "1941", "2517", "3214", "4048", "5036", "6196", "7547", "9109", "10903", "12951", "15276", "17902", "20854", "24158", "27841", "31931", "36457", "41449", "46938", "52956", "59536", "66712", "74519", "82993", "92171", "102091", "112792", "124314", "136698" ]
[ "nonn", "easy", "nice" ]
229
1
2
[ "A000012", "A000027", "A000124", "A000125", "A000127", "A002522", "A005408", "A006261", "A007318", "A008859", "A008863", "A016813", "A058331", "A080856", "A086514", "A161701", "A161702", "A161703", "A161704", "A161706", "A161707", "A161708", "A161710", "A161711", "A161712", "A161713", "A161715", "A219531", "A223718" ]
[ "M1119", "N0427" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000127.seq
8cbc6662967e3c7105b3ad0cae58e2b0
A000128
A nonlinear binomial sum.
[ "1", "2", "4", "8", "16", "31", "58", "105", "185", "319", "541", "906", "1503", "2476", "4058", "6626", "10790", "17537", "28464", "46155", "74791", "121137", "196139", "317508", "513901", "831686", "1345888", "2177900", "3524140", "5702419", "9226966", "14929821", "24157253", "39087571", "63245353", "102333486" ]
[ "nonn", "easy" ]
62
1
2
[ "A000045", "A000071", "A000126", "A000128" ]
[ "M1120", "N0428" ]
N. J. A. Sloane
2025-01-05T19:51:30
oeisdata/seq/A000/A000128.seq
cb8afc4b57f2ab668339aee0a5bdca80
A000129
Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
[ "0", "1", "2", "5", "12", "29", "70", "169", "408", "985", "2378", "5741", "13860", "33461", "80782", "195025", "470832", "1136689", "2744210", "6625109", "15994428", "38613965", "93222358", "225058681", "543339720", "1311738121", "3166815962", "7645370045", "18457556052", "44560482149", "107578520350", "259717522849" ]
[ "nonn", "easy", "core", "cofr", "nice", "frac", "changed" ]
1,065
0
3
[ "A000045", "A000129", "A001076", "A001333", "A001622", "A002203", "A002532", "A002533", "A002605", "A005409", "A005668", "A006190", "A006497", "A008555", "A014176", "A015518", "A015519", "A021083", "A026150", "A034867", "A038207", "A041025", "A041041", "A041061", "A041085", "A041113", "A041145", "A041181", "A046717", "A048739", "A049666", "A051927", "A052918", "A054413", "A054456", "A063727", "A073133", "A077985", "A083098", "A083099", "A083100", "A084057", "A096669", "A096670", "A097075", "A097076", "A098316", "A099371", "A131980", "A133156", "A135387", "A140455", "A143808", "A153346", "A154325", "A154597", "A157103", "A172236", "A175181", "A178765", "A214027", "A214028", "A243399", "A352361" ]
[ "M1413", "N0552" ]
N. J. A. Sloane
2025-04-19T03:50:01
oeisdata/seq/A000/A000129.seq
be68fd4030bca19b792acad3fb0a933b
A000130
One-half the number of permutations of length n with exactly 1 rising or falling successions.
[ "0", "0", "1", "2", "5", "20", "115", "790", "6217", "55160", "545135", "5938490", "70686805", "912660508", "12702694075", "189579135710", "3019908731105", "51139445487680", "917345570926087", "17376071107513090", "346563420097249645", "7259714390232227300", "159352909727731210835", "3657569576966074846118" ]
[ "nonn" ]
25
0
4
[ "A000130", "A002464", "A010028", "A086852", "A086853" ]
[ "M1528", "N0598" ]
N. J. A. Sloane
2015-03-27T03:23:48
oeisdata/seq/A000/A000130.seq
ef4ce867926dc758c29649fae968c77c
A000131
Number of asymmetrical dissections of n-gon.
[ "2", "5", "21", "61", "214", "669", "2240", "7330", "24695", "83257", "284928", "981079", "3410990", "11937328", "42075242", "149171958", "531866972", "1905842605", "6861162880", "24805692978", "90035940227", "327987890608", "1198853954688", "4395797189206", "16165195705544", "59609156824273", "220373268471398", "816677398144221" ]
[ "nonn" ]
40
7
1
[ "A000063", "A000131" ]
[ "M1535", "N0599" ]
N. J. A. Sloane
2015-10-08T15:21:21
oeisdata/seq/A000/A000131.seq
05cb0f31cdb6ef4981439b99c56f608a
A000132
Number of ways of writing n as a sum of 5 squares.
[ "1", "10", "40", "80", "90", "112", "240", "320", "200", "250", "560", "560", "400", "560", "800", "960", "730", "480", "1240", "1520", "752", "1120", "1840", "1600", "1200", "1210", "2000", "2240", "1600", "1680", "2720", "3200", "1480", "1440", "3680", "3040", "2250", "2800", "3280", "4160", "2800", "1920", "4320", "5040", "2800", "3472", "5920" ]
[ "nonn", "easy" ]
82
0
2
[ "A000118", "A000132", "A025429", "A122141", "A286815" ]
null
N. J. A. Sloane
2024-06-23T04:09:39
oeisdata/seq/A000/A000132.seq
1db4fe9b0110c84e5c8234cc40cf87ad
A000133
Number of Boolean functions of n variables.
[ "2", "5", "30", "2288", "67172352", "144115192303714304", "1329227995784915891206435945914040320", "226156424291633194186662080095093570364871077725232774230036394136943198208" ]
[ "nonn", "easy", "nice" ]
29
1
1
null
[ "M1547", "N0604" ]
N. J. A. Sloane
2020-09-04T13:49:29
oeisdata/seq/A000/A000133.seq
4606b5697bf782f658bf3d98dcb7fb42
A000134
Positive zeros of Bessel function of order 0 rounded to nearest integer.
[ "2", "6", "9", "12", "15", "18", "21", "24", "27", "31", "34", "37", "40", "43", "46", "49", "53", "56", "59", "62", "65", "68", "71", "75", "78", "81", "84", "87", "90", "93", "97", "100", "103", "106", "109", "112", "115", "119", "122", "125", "128", "131", "134", "137", "141", "144", "147", "150", "153", "156", "159", "163", "166", "169", "172", "175", "178", "181", "185", "188" ]
[ "nonn" ]
27
1
1
null
[ "M1570", "N0613" ]
N. J. A. Sloane
2018-05-08T15:11:52
oeisdata/seq/A000/A000134.seq
37fb5af96f39e436f96850c97f343d69
A000135
Number of partitions into non-integral powers.
[ "1", "2", "6", "13", "24", "42", "73", "125", "204", "324", "511", "801", "1228", "1856", "2780", "4135", "6084", "8873", "12847", "18481", "26416", "37473", "52871", "74216", "103596", "143841", "198839", "273654", "374987", "511735", "695559", "941932", "1271139", "1709474", "2291195", "3061385", "4078152", "5416322" ]
[ "nonn" ]
18
1
2
[ "A000135", "A000148", "A000158", "A000160" ]
[ "M1595", "N0622" ]
N. J. A. Sloane
2015-06-27T17:54:46
oeisdata/seq/A000/A000135.seq
4b427589abda581851808eef1153dae7
A000136
Number of ways of folding a strip of n labeled stamps.
[ "1", "2", "6", "16", "50", "144", "462", "1392", "4536", "14060", "46310", "146376", "485914", "1557892", "5202690", "16861984", "56579196", "184940388", "622945970", "2050228360", "6927964218", "22930109884", "77692142980", "258360586368", "877395996200", "2929432171328", "9968202968958", "33396290888520", "113837957337750" ]
[ "nonn" ]
103
1
2
[ "A000136", "A000560" ]
[ "M1614", "N0630" ]
N. J. A. Sloane
2025-04-04T15:45:08
oeisdata/seq/A000/A000136.seq
278c3ff615cf84235756a782c4fbadb4
A000137
Series-parallel numbers.
[ "1", "2", "6", "18", "58", "186", "614", "2034", "6818", "22970", "77858", "264970", "905294", "3102434", "10661370", "36722642", "126752218", "438294018", "1518032598", "5265341314", "18286911130", "63586988434", "221342104842", "771235606050", "2689688538646", "9388096331642" ]
[ "nonn", "easy" ]
31
1
2
[ "A000084", "A000137", "A036654", "A036655", "A058756" ]
[ "M1625", "N0636" ]
N. J. A. Sloane
2017-08-08T08:44:24
oeisdata/seq/A000/A000137.seq
754791f465fc0faf00bd15662c131dda
A000138
Expansion of e.g.f. exp(-x^4/4)/(1-x).
[ "1", "1", "2", "6", "18", "90", "540", "3780", "31500", "283500", "2835000", "31185000", "372972600", "4848643800", "67881013200", "1018215198000", "16294848570000", "277012425690000", "4986223662420000", "94738249585980000", "1894745192712372000", "39789649046959812000", "875372279033115864000" ]
[ "nonn", "easy" ]
49
0
3
[ "A000090", "A000138", "A000142", "A000266", "A060725", "A060726", "A060727" ]
[ "M1635", "N0638" ]
N. J. A. Sloane
2024-03-04T19:36:38
oeisdata/seq/A000/A000138.seq
9eda5ffa15361fa5ba94572d11b649d0
A000139
a(n) = 2*(3*n)! / ((2*n+1)!*(n+1)!).
[ "2", "1", "2", "6", "22", "91", "408", "1938", "9614", "49335", "260130", "1402440", "7702632", "42975796", "243035536", "1390594458", "8038677054", "46892282815", "275750636070", "1633292229030", "9737153323590", "58392041019795", "352044769046880", "2132866978427640" ]
[ "nonn", "easy", "nice" ]
251
0
1
[ "A000139", "A000142", "A000309", "A001764", "A004677", "A005802", "A006335", "A121545", "A210664", "A218473", "A233389" ]
[ "M1660", "N0651" ]
N. J. A. Sloane, entry revised Apr 24 2012
2025-01-08T09:07:32
oeisdata/seq/A000/A000139.seq
156b88737e34e82956235fa8eee404f0
A000140
Kendall-Mann numbers: the most common number of inversions in a permutation on n letters is floor(n*(n-1)/4); a(n) is the number of permutations with this many inversions.
[ "1", "1", "2", "6", "22", "101", "573", "3836", "29228", "250749", "2409581", "25598186", "296643390", "3727542188", "50626553988", "738680521142", "11501573822788", "190418421447330", "3344822488498265", "62119523114983224", "1214967840930909302", "24965661442811799655", "538134522243713149122" ]
[ "nonn", "easy", "core", "nice" ]
160
1
3
[ "A000124", "A000140", "A001147", "A008302", "A128566", "A181609", "A186888" ]
[ "M1665", "N0655" ]
N. J. A. Sloane
2024-08-02T04:32:01
oeisdata/seq/A000/A000140.seq
dd062fc7054197530bd5083890b513e7
A000141
Number of ways of writing n as a sum of 6 squares.
[ "1", "12", "60", "160", "252", "312", "544", "960", "1020", "876", "1560", "2400", "2080", "2040", "3264", "4160", "4092", "3480", "4380", "7200", "6552", "4608", "8160", "10560", "8224", "7812", "10200", "13120", "12480", "10104", "14144", "19200", "16380", "11520", "17400", "24960", "18396", "16440", "24480", "27200" ]
[ "nonn", "easy", "nice" ]
80
0
2
[ "A000141", "A002173", "A050470", "A122141", "A286815", "A319574" ]
null
N. J. A. Sloane
2024-06-21T12:39:18
oeisdata/seq/A000/A000141.seq
7e4162d5cffc6ed5cda277d93fbff3dc
A000142
Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters).
[ "1", "1", "2", "6", "24", "120", "720", "5040", "40320", "362880", "3628800", "39916800", "479001600", "6227020800", "87178291200", "1307674368000", "20922789888000", "355687428096000", "6402373705728000", "121645100408832000", "2432902008176640000", "51090942171709440000", "1124000727777607680000" ]
[ "core", "easy", "nonn", "nice" ]
837
0
3
[ "A000142", "A000165", "A000169", "A001013", "A001044", "A001563", "A003319", "A003422", "A007623", "A009445", "A010050", "A012245", "A033312", "A034886", "A038507", "A045509", "A045510", "A045511", "A045516", "A045517", "A045518", "A045519", "A045520", "A045521", "A045522", "A045523", "A045524", "A045525", "A045526", "A045527", "A045528", "A045529", "A047920", "A048631", "A052186", "A053657", "A063992", "A075513", "A144107", "A144108", "A152917", "A163176", "A173280", "A230960", "A230961", "A233589", "A245334", "A249026", "A258773", "A282021" ]
[ "M1675", "N0659" ]
N. J. A. Sloane
2025-03-19T08:22:28
oeisdata/seq/A000/A000142.seq
5d20934f90f9f3f604ca860051665fa3
A000143
Number of ways of writing n as a sum of 8 squares.
[ "1", "16", "112", "448", "1136", "2016", "3136", "5504", "9328", "12112", "14112", "21312", "31808", "35168", "38528", "56448", "74864", "78624", "84784", "109760", "143136", "154112", "149184", "194688", "261184", "252016", "246176", "327040", "390784", "390240", "395136", "476672", "599152", "596736", "550368", "693504", "859952" ]
[ "nonn", "easy" ]
107
0
2
[ "A000118", "A000122", "A000141", "A000143", "A000700", "A004018", "A008457", "A010054", "A010815", "A035016", "A121373", "A122141", "A286815" ]
null
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000143.seq
b2521b2c6519e67cc46f2188cd28da98
A000144
Number of ways of writing n as a sum of 10 squares.
[ "1", "20", "180", "960", "3380", "8424", "16320", "28800", "52020", "88660", "129064", "175680", "262080", "386920", "489600", "600960", "840500", "1137960", "1330420", "1563840", "2050344", "2611200", "2986560", "3358080", "4194240", "5318268", "5878440", "6299520", "7862400", "9619560" ]
[ "nonn", "easy" ]
52
0
2
[ "A000144", "A122141", "A286815", "A319574" ]
null
N. J. A. Sloane
2019-11-01T11:32:24
oeisdata/seq/A000/A000144.seq
a2e33ff492f306c265fce787c1e3f65b
A000145
Number of ways of writing n as a sum of 12 squares.
[ "1", "24", "264", "1760", "7944", "25872", "64416", "133056", "253704", "472760", "825264", "1297056", "1938336", "2963664", "4437312", "6091584", "8118024", "11368368", "15653352", "19822176", "24832944", "32826112", "42517728", "51425088", "61903776", "78146664", "98021616" ]
[ "nonn", "easy" ]
55
0
2
[ "A000145", "A000735", "A029751", "A122141", "A286815", "A319574" ]
null
N. J. A. Sloane
2022-09-08T08:44:27
oeisdata/seq/A000/A000145.seq
a2a96aadb8021298d584fd406b797b89
A000146
From von Staudt-Clausen representation of Bernoulli numbers: a(n) = Bernoulli(2n) + Sum_{(p-1)|2n} 1/p.
[ "1", "1", "1", "1", "1", "1", "2", "-6", "56", "-528", "6193", "-86579", "1425518", "-27298230", "601580875", "-15116315766", "429614643062", "-13711655205087", "488332318973594", "-19296579341940067", "841693047573682616", "-40338071854059455412", "2115074863808199160561", "-120866265222965259346026" ]
[ "sign", "nice", "easy" ]
71
1
7
[ "A000146", "A002882", "A003245", "A127187", "A127188" ]
[ "M1717", "N0680" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000146.seq
3ad7cfe472d72c50ea651ac0e017c2cd
A000147
Number of trees of diameter 5.
[ "0", "0", "0", "0", "0", "1", "2", "7", "14", "32", "58", "110", "187", "322", "519", "839", "1302", "2015", "3032", "4542", "6668", "9738", "14006", "20036", "28324", "39830", "55473", "76875", "105692", "144629", "196585", "266038", "357952", "479664", "639519", "849425", "1123191", "1479972", "1942284", "2540674", "3311415" ]
[ "nonn" ]
32
1
7
[ "A000147", "A000251", "A034853" ]
[ "M1741", "N0690" ]
N. J. A. Sloane
2017-04-03T04:22:36
oeisdata/seq/A000/A000147.seq
36beefc18879a22d943a7aca3bf6c1e4
A000148
Number of partitions into non-integral powers.
[ "1", "2", "7", "15", "28", "45", "70", "100", "138", "183", "242", "310", "388", "481", "583", "701", "838", "984", "1152", "1337", "1535", "1757", "2001", "2262", "2545", "2855", "3183", "3540", "3926", "4335", "4770", "5233", "5728", "6248", "6801", "7388", "8005", "8658", "9345", "10064", "10824", "11620", "12452", "13324", "14236" ]
[ "nonn" ]
34
2
2
[ "A000148", "A000158", "A000160", "A000327" ]
[ "M1743", "N0691" ]
N. J. A. Sloane
2024-12-10T12:10:56
oeisdata/seq/A000/A000148.seq
51aa8829c8f590a4e4c83a048ea5e098
A000149
a(n) = floor(e^n).
[ "1", "2", "7", "20", "54", "148", "403", "1096", "2980", "8103", "22026", "59874", "162754", "442413", "1202604", "3269017", "8886110", "24154952", "65659969", "178482300", "485165195", "1318815734", "3584912846", "9744803446", "26489122129", "72004899337", "195729609428", "532048240601", "1446257064291" ]
[ "nonn", "easy" ]
56
0
2
[ "A000079", "A000149", "A000227", "A000244", "A001113", "A001671", "A003619", "A064780", "A116472" ]
[ "M1751", "N0695" ]
N. J. A. Sloane
2024-07-30T02:16:48
oeisdata/seq/A000/A000149.seq
4ae4ef266e574f6b5fd55a524d7cffc0
A000150
Number of dissections of an n-gon, rooted at an exterior edge, asymmetric with respect to that edge.
[ "0", "0", "1", "2", "7", "20", "66", "212", "715", "2424", "8398", "29372", "104006", "371384", "1337220", "4847208", "17678835", "64821680", "238819350", "883629164", "3282060210", "12233125112", "45741281820", "171529777432", "644952073662", "2430973096720", "9183676536076" ]
[ "nonn", "nice", "easy" ]
71
0
4
[ "A000150", "A005430", "A007595", "A051168" ]
[ "M1753", "N0696" ]
N. J. A. Sloane
2022-12-31T01:32:52
oeisdata/seq/A000/A000150.seq
eae3cd43a08b1381d5fdb391c951df3a
A000151
Number of oriented rooted trees with n nodes. Also rooted trees with n nodes and 2-colored non-root nodes.
[ "1", "2", "7", "26", "107", "458", "2058", "9498", "44947", "216598", "1059952", "5251806", "26297238", "132856766", "676398395", "3466799104", "17873508798", "92630098886", "482292684506", "2521610175006", "13233573019372", "69687684810980", "368114512431638", "1950037285256658", "10357028326495097", "55140508518522726", "294219119815868952", "1573132563600386854", "8427354035116949486", "45226421721391554194" ]
[ "nonn", "eigen", "nice" ]
92
1
2
[ "A000151", "A000238", "A005750", "A005751", "A038055", "A242249", "A245870" ]
[ "M1770", "N0701" ]
N. J. A. Sloane
2020-12-26T09:56:22
oeisdata/seq/A000/A000151.seq
a268ec56fe1061fdedaadd8e375dfde8
A000152
Number of ways of writing n as a sum of 16 squares.
[ "1", "32", "480", "4480", "29152", "140736", "525952", "1580800", "3994080", "8945824", "18626112", "36714624", "67978880", "118156480", "197120256", "321692928", "509145568", "772845120", "1143441760", "1681379200", "2428524096", "3392205824", "4658843520", "6411152640" ]
[ "nonn", "easy" ]
42
0
2
[ "A000152", "A022047", "A122141", "A286815", "A319574" ]
null
N. J. A. Sloane
2018-10-02T05:07:05
oeisdata/seq/A000/A000152.seq
4db3c5473578078ed429b6703423cb1a
A000153
a(n) = n*a(n-1) + (n-2)*a(n-2), with a(0) = 0, a(1) = 1.
[ "0", "1", "2", "7", "32", "181", "1214", "9403", "82508", "808393", "8743994", "103459471", "1328953592", "18414450877", "273749755382", "4345634192131", "73362643649444", "1312349454922513", "24796092486996338", "493435697986613143", "10315043624498196944" ]
[ "nonn", "easy" ]
119
0
3
[ "A000153", "A000255", "A000261", "A001710", "A001909", "A001910", "A055790", "A086764", "A090010", "A090012", "A090016" ]
[ "M1791", "N0706" ]
N. J. A. Sloane
2024-07-30T05:33:59
oeisdata/seq/A000/A000153.seq
52495acaf5a2328b61b60371dbfd0d49
A000154
Erroneous version of A003713.
[ "1", "1", "2", "7", "35", "228", "1834", "17382", "195866", "2487832", "35499576", "562356672", "9794156448", "186025364016", "3826961710272", "84775065603888", "2011929826983504" ]
[ "dead" ]
16
0
3
null
[ "M1798" ]
null
2017-10-23T18:00:48
oeisdata/seq/A000/A000154.seq
fac44cbfde27451d44bf80b3aaf341c5
A000155
Nearest integer to modified Bessel function K_n(1).
[ "0", "1", "2", "7", "44", "361", "3654", "44207", "622552", "10005041", "180713290", "3624270839", "79914671748", "1921576392793", "50040900884366", "1403066801155039", "42142044935535536", "1349948504738292193", "45940391206037470098" ]
[ "nonn" ]
41
0
3
null
[ "M1810", "N0716" ]
N. J. A. Sloane
2022-06-01T01:48:14
oeisdata/seq/A000/A000155.seq
48906a505f2aa32d092d6cb698014476
A000156
Number of ways of writing n as a sum of 24 squares.
[ "1", "48", "1104", "16192", "170064", "1362336", "8662720", "44981376", "195082320", "721175536", "2319457632", "6631997376", "17231109824", "41469483552", "93703589760", "200343312768", "407488018512", "793229226336", "1487286966928", "2697825744960", "4744779429216" ]
[ "nonn", "easy" ]
63
0
2
[ "A000156", "A122141", "A286815", "A319574" ]
null
N. J. A. Sloane
2018-10-02T05:03:10
oeisdata/seq/A000/A000156.seq
671dcf41a8a4d1b37f9b0f86208d3e69
A000157
Number of Boolean functions of n variables.
[ "1", "2", "7", "111", "308063", "100126976263592", "131867858014413288241233435594064", "2804519150441879896741320496043335469582478995067528608051651559815168" ]
[ "nonn" ]
30
1
2
[ "A000157", "A000370" ]
[ "M1818", "N0721" ]
N. J. A. Sloane
2019-01-13T15:57:29
oeisdata/seq/A000/A000157.seq
2bbf799ee5c188f145248b54ae4a37e2
A000158
Number of partitions into non-integral powers.
[ "1", "2", "8", "19", "41", "78", "134", "218", "339", "506", "730", "1023", "1397", "1884", "2477", "3218", "4118", "5192", "6486", "8010", "9795", "11888", "14302", "17066", "20256", "23889", "27999", "32637", "37863", "43695", "50218", "57495", "65545", "74431", "84257", "95030", "106840", "119799", "133941", "149311", "166071" ]
[ "nonn" ]
16
3
2
[ "A000148", "A000158", "A000160", "A000234" ]
[ "M1830", "N0726" ]
N. J. A. Sloane
2015-06-27T17:50:28
oeisdata/seq/A000/A000158.seq
dacedb221b4d6ff7d604947551cd3878
A000159
Coefficients of ménage hit polynomials.
[ "2", "8", "20", "152", "994", "7888", "70152", "695760", "7603266", "90758872", "1174753372", "16386899368", "245046377410", "3910358788256", "66323124297872", "1191406991067168", "22596344660865282", "451208920617687720", "9461897733571886372", "207894669895136763704", "4776019866458134139042" ]
[ "nonn" ]
50
3
1
[ "A000159", "A000179", "A000425", "A058087" ]
[ "M1834", "N0728" ]
N. J. A. Sloane, Simon Plouffe
2019-06-10T23:15:14
oeisdata/seq/A000/A000159.seq
5e41e216fb36f79ed13f601adae94db9
A000160
Number of partitions into non-integral powers.
[ "1", "2", "8", "21", "48", "99", "186", "330", "556", "895", "1397", "2107", "3097", "4459", "6264", "8644", "11760", "15742", "20790", "27128", "34993", "44664", "56473", "70784", "87995", "108564", "132970", "161828", "195686", "235274", "281349", "334682", "396202", "466849", "547712", "639935", "744716", "863443" ]
[ "nonn" ]
15
4
2
null
[ "M1835", "N0729" ]
N. J. A. Sloane
2015-06-27T17:50:57
oeisdata/seq/A000/A000160.seq
34ac60ed239382f33f199052ad5e3cb2
A000161
Number of partitions of n into 2 squares.
[ "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "2", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "2", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "2", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "2", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "2", "1", "0", "0", "1", "0", "1", "0" ]
[ "nonn", "core", "easy", "nice" ]
85
0
26
[ "A000161", "A000164", "A000174", "A000290", "A000925", "A001481", "A002635", "A002654", "A010052", "A025426", "A025427", "A025428", "A063725", "A247367" ]
null
N. J. A. Sloane
2022-09-09T02:33:47
oeisdata/seq/A000/A000161.seq
b6db4aced934e287e993e86d182fcd01
A000162
Number of 3-dimensional polyominoes (or polycubes) with n cells.
[ "1", "1", "2", "8", "29", "166", "1023", "6922", "48311", "346543", "2522522", "18598427", "138462649", "1039496297", "7859514470", "59795121480", "457409613979", "3516009200564", "27144143923583", "210375361379518", "1636229771639924", "12766882202755783" ]
[ "nonn", "nice", "hard", "more" ]
99
1
3
[ "A000162", "A001931", "A007743", "A038119", "A066453", "A371397" ]
[ "M1845", "N0731" ]
N. J. A. Sloane and J. H. Conway
2025-03-13T09:45:17
oeisdata/seq/A000/A000162.seq
23451f899d46d1294a6c05ae990ae508
A000163
Series-parallel numbers.
[ "2", "8", "34", "136", "538", "2080", "7970", "30224", "113874", "426520", "1590338", "5906640", "21866794", "80725280", "297292610", "1092539736", "4007553922", "14675748416", "53663197698", "195962433328", "714734393378", "2603994002280", "9477643739746", "34463730424720" ]
[ "nonn" ]
19
2
1
null
[ "M1852", "N0732" ]
N. J. A. Sloane
2016-02-09T07:39:08
oeisdata/seq/A000/A000163.seq
4a70c78112030d797eb6fe508b6591df
A000164
Number of partitions of n into 3 squares (allowing part zero).
[ "1", "1", "1", "1", "1", "1", "1", "0", "1", "2", "1", "1", "1", "1", "1", "0", "1", "2", "2", "1", "1", "1", "1", "0", "1", "2", "2", "2", "0", "2", "1", "0", "1", "2", "2", "1", "2", "1", "2", "0", "1", "3", "1", "1", "1", "2", "1", "0", "1", "2", "3", "2", "1", "2", "3", "0", "1", "2", "1", "2", "0", "2", "2", "0", "1", "3", "3", "1", "2", "2", "1", "0", "2", "2", "3", "2", "1", "2", "1", "0", "1", "4", "2", "2", "1", "2", "3", "0", "1", "4", "3", "1", "0", "1", "2", "0", "1", "2", "3", "3", "2", "4", "2", "0", "2" ]
[ "nonn" ]
44
0
10
[ "A000161", "A000164", "A000174", "A002635", "A004215", "A005875", "A016727", "A094942", "A124966" ]
null
N. J. A. Sloane
2022-10-17T01:45:44
oeisdata/seq/A000/A000164.seq
aa1f1adedfa727b8c9ad8cc3901dc11f
A000165
Double factorial of even numbers: (2n)!! = 2^n*n!.
[ "1", "2", "8", "48", "384", "3840", "46080", "645120", "10321920", "185794560", "3715891200", "81749606400", "1961990553600", "51011754393600", "1428329123020800", "42849873690624000", "1371195958099968000", "46620662575398912000", "1678343852714360832000", "63777066403145711616000" ]
[ "nonn", "easy", "nice" ]
334
0
2
[ "A000079", "A000108", "A000111", "A000142", "A000165", "A001044", "A001147", "A001563", "A001804", "A001805", "A001806", "A001807", "A001813", "A001907", "A002454", "A006882", "A007060", "A008277", "A008544", "A010050", "A019774", "A028326", "A028338", "A032184", "A035038", "A039683", "A039757", "A047053", "A047055", "A047058", "A047657", "A060187", "A075271", "A084947", "A084948", "A084949", "A092605", "A133314", "A145271", "A193229", "A208057", "A329070" ]
[ "M1878", "N0742" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000165.seq
aa35b164b7966159a01c5a1240f4aef1
A000166
Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
[ "1", "0", "1", "2", "9", "44", "265", "1854", "14833", "133496", "1334961", "14684570", "176214841", "2290792932", "32071101049", "481066515734", "7697064251745", "130850092279664", "2355301661033953", "44750731559645106", "895014631192902121", "18795307255050944540", "413496759611120779881", "9510425471055777937262" ]
[ "core", "nonn", "easy", "nice", "changed" ]
711
0
4
[ "A000045", "A000108", "A000110", "A000142", "A000166", "A000204", "A000240", "A000255", "A000387", "A000449", "A000475", "A000522", "A000757", "A001120", "A001277", "A002467", "A002469", "A002741", "A003221", "A008279", "A008290", "A008291", "A008305", "A010027", "A033030", "A038205", "A047865", "A053556", "A053557", "A053871", "A068106", "A068985", "A068996", "A086764", "A088991", "A088992", "A092582", "A094216", "A094638", "A099731", "A100492", "A101032", "A101033", "A101559", "A101560", "A103360", "A103361", "A103816", "A129135", "A159610", "A216963", "A281682", "A323671", "A334715", "A364068" ]
[ "M1937", "N0766" ]
N. J. A. Sloane
2025-04-21T13:24:00
oeisdata/seq/A000/A000166.seq
b772b8f1a8750bfb8ea5b62030cd26bf
A000167
Nearest integer to modified Bessel function K_n(2).
[ "0", "0", "0", "1", "2", "9", "49", "306", "2188", "17810", "162482", "1642635", "18231462", "220420179", "2883693795", "40592133316", "611765693528", "9828843229764", "167702100599524", "3028466654021205", "57708568527002410", "1157199837194069405" ]
[ "nonn" ]
33
0
5
null
[ "M1938", "N0767" ]
N. J. A. Sloane
2023-12-09T07:04:23
oeisdata/seq/A000/A000167.seq
6783048dc38761a0ee9f4ee389ff98cc
A000168
a(n) = 2*3^n*(2*n)!/(n!*(n+2)!).
[ "1", "2", "9", "54", "378", "2916", "24057", "208494", "1876446", "17399772", "165297834", "1602117468", "15792300756", "157923007560", "1598970451545", "16365932856990", "169114639522230", "1762352559231660", "18504701871932430", "195621134074714260", "2080697516976506220", "22254416920705240440", "239234981897581334730", "2583737804493878415084" ]
[ "nonn", "nice", "easy" ]
208
0
2
[ "A000168", "A000260", "A000309", "A000698", "A000699", "A002005", "A005470", "A006300", "A006301", "A062980", "A101486", "A104742", "A215402", "A238355", "A238356", "A238357", "A238358", "A238359", "A238360", "A267827" ]
[ "M1940", "N0768" ]
N. J. A. Sloane
2024-08-23T03:15:08
oeisdata/seq/A000/A000168.seq
ff872bd87cb24c53b14c40823a195f76
A000169
Number of labeled rooted trees with n nodes: n^(n-1).
[ "1", "2", "9", "64", "625", "7776", "117649", "2097152", "43046721", "1000000000", "25937424601", "743008370688", "23298085122481", "793714773254144", "29192926025390625", "1152921504606846976", "48661191875666868481", "2185911559738696531968", "104127350297911241532841", "5242880000000000000000000" ]
[ "easy", "core", "nonn", "nice" ]
313
1
2
[ "A000055", "A000081", "A000142", "A000169", "A000272", "A000312", "A002061", "A002720", "A007778", "A007830", "A008785", "A008791", "A051129", "A052746", "A052756", "A052764", "A052789", "A053506", "A053509", "A055302", "A055860", "A098686", "A130293", "A247363", "A248120", "A262974", "A275549", "A275558" ]
[ "M1946", "N0771" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000169.seq
f8bd1a6e13c531f482ae0df258c0037f
A000170
Number of ways of placing n nonattacking queens on an n X n board.
[ "1", "1", "0", "0", "2", "10", "4", "40", "92", "352", "724", "2680", "14200", "73712", "365596", "2279184", "14772512", "95815104", "666090624", "4968057848", "39029188884", "314666222712", "2691008701644", "24233937684440", "227514171973736", "2207893435808352", "22317699616364044", "234907967154122528" ]
[ "nonn", "hard", "nice" ]
263
0
5
[ "A000170", "A002562", "A006717", "A036464", "A047659", "A051906", "A061994", "A065256", "A099152", "A108792", "A140393", "A176186", "A319284", "A348129" ]
[ "M1958", "N0775" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000170.seq
9b6940c07dff8f088055180505d9d6f2
A000171
Number of self-complementary graphs with n nodes.
[ "1", "0", "0", "1", "2", "0", "0", "10", "36", "0", "0", "720", "5600", "0", "0", "703760", "11220000", "0", "0", "9168331776", "293293716992", "0", "0", "1601371799340544", "102484848265030656", "0", "0", "3837878966366932639744", "491247277315343649710080", "0", "0" ]
[ "nonn", "nice" ]
68
1
5
[ "A000171", "A008406", "A047660", "A047832", "A051251" ]
[ "M0014", "N0780" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000171.seq
fbcb80f7d59727cc507bb06940db299a
A000172
The Franel number a(n) = Sum_{k = 0..n} binomial(n,k)^3.
[ "1", "2", "10", "56", "346", "2252", "15184", "104960", "739162", "5280932", "38165260", "278415920", "2046924400", "15148345760", "112738423360", "843126957056", "6332299624282", "47737325577620", "361077477684436", "2739270870994736", "20836827035351596", "158883473753259752", "1214171997616258240" ]
[ "nonn", "easy", "nice" ]
377
0
2
[ "A000079", "A000172", "A000578", "A000984", "A002893", "A002895", "A005258", "A005259", "A005260", "A005261", "A006077", "A006480", "A007318", "A033581", "A036917", "A052144", "A063007", "A069865", "A081085", "A093388", "A094424", "A096191", "A125143", "A133370", "A141057", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A181543", "A182421", "A182422", "A182446", "A182447", "A183204", "A189791", "A214262", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A279619", "A290575", "A290576", "A291275", "A291284", "A342294", "A342295", "A372307" ]
[ "M1971", "N0781" ]
N. J. A. Sloane
2025-04-04T15:45:11
oeisdata/seq/A000/A000172.seq
8abdb2c93a85e794969709d5787e80e9
A000173
Unitary-sociable numbers (smallest member of each cycle).
[ "30", "1482", "2418", "24180", "35238", "263820", "395730", "473298", "698130", "763620", "2212026", "2233554", "172459210", "209524210", "341354790", "384121920", "525150234", "530946330", "582129630", "1799281330", "2069510520", "2514290520", "3344596854", "5251502340" ]
[ "nonn", "nice" ]
19
1
1
[ "A000173", "A003416", "A034444", "A097323" ]
null
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000173.seq
f60e34ced78596bf2f3ac2d664604f95
A000174
Number of partitions of n into 5 squares.
[ "1", "1", "1", "1", "2", "2", "1", "1", "2", "2", "2", "2", "2", "3", "2", "1", "3", "3", "3", "3", "4", "3", "3", "2", "2", "4", "4", "4", "4", "5", "3", "3", "4", "3", "5", "5", "5", "6", "5", "3", "5", "5", "5", "6", "5", "6", "5", "4", "4", "6", "7", "6", "8", "8", "7", "5", "6", "5", "8", "8", "4", "9", "7", "6", "7", "7", "8", "9", "9", "7", "9", "6", "7", "8", "10", "9", "9", "11", "7", "8", "8", "8", "11", "11", "9", "12", "11", "7", "9", "9", "12", "13", "9", "10", "11", "8", "6", "10", "13", "13", "13" ]
[ "nonn" ]
40
0
5
[ "A000161", "A000164", "A000174", "A000177", "A002635", "A010052", "A025422", "A025423", "A025424", "A025425", "A025429", "A295160" ]
null
N. J. A. Sloane
2025-03-25T10:11:34
oeisdata/seq/A000/A000174.seq
de2ee4f099d4e74fc19571b000afd3cf
A000175
Related to zeros of Bessel function.
[ "1", "1", "2", "11", "38", "946", "4580", "202738", "3786092", "261868876", "1992367192", "2381255244240", "21411255538848", "2902625722978656", "451716954504285504", "319933105641374465472", "3761845343198709705600" ]
[ "nonn" ]
29
1
3
null
[ "M2000", "N0790" ]
N. J. A. Sloane
2016-08-23T04:09:31
oeisdata/seq/A000/A000175.seq
821becc1d14b59c4516047a777b79b12
A000176
Generalized tangent numbers d_(n,2).
[ "2", "11", "46", "128", "272", "522", "904", "1408", "2160", "3154", "4306", "5888", "7888", "10012", "12888", "16384", "19680", "24354", "29866", "34816", "41888", "49778", "56744", "66816", "78000", "87358", "100602", "115712", "128112", "145804", "165712", "180224", "203040", "228964", "246932", "276480" ]
[ "nonn" ]
31
1
1
[ "A000061", "A000176", "A000488", "A000518" ]
[ "M2001", "N0791" ]
N. J. A. Sloane
2024-07-28T10:05:52
oeisdata/seq/A000/A000176.seq
9e9f772b94fc725bf4014b9d2fde2792
A000177
Number of partitions of n into 6 squares.
[ "1", "1", "1", "1", "2", "2", "2", "1", "2", "3", "2", "2", "3", "3", "3", "2", "3", "4", "4", "3", "5", "5", "4", "3", "4", "5", "5", "5", "5", "7", "6", "4", "5", "6", "6", "6", "9", "7", "8", "6", "6", "9", "7", "7", "9", "10", "8", "7", "7", "9", "10", "9", "11", "12", "13", "8", "10", "11", "10", "11", "11", "12", "13", "11", "9", "14", "13", "12", "16", "14", "14", "12", "13", "13", "15", "15", "15", "18", "16", "13", "14", "18", "15", "17", "20", "17", "21", "15", "15" ]
[ "nonn" ]
13
0
5
null
null
N. J. A. Sloane
2016-08-28T18:18:32
oeisdata/seq/A000/A000177.seq
047e0b3cb1d219dd214ffebde0da4c0e
A000178
Superfactorials: product of first n factorials.
[ "1", "1", "2", "12", "288", "34560", "24883200", "125411328000", "5056584744960000", "1834933472251084800000", "6658606584104736522240000000", "265790267296391946810949632000000000", "127313963299399416749559771247411200000000000", "792786697595796795607377086400871488552960000000000000" ]
[ "nonn", "nice", "easy", "changed" ]
329
0
3
[ "A000085", "A000110", "A000142", "A000178", "A000292", "A000296", "A001906", "A002109", "A005425", "A005493", "A005494", "A036561", "A036740", "A045379", "A051675", "A055462", "A087316", "A098694", "A098695", "A113122", "A113153", "A113154", "A113170", "A113173", "A113208", "A113231", "A113257", "A113258", "A113271", "A113320", "A113336", "A113475", "A113492", "A113497", "A113498", "A113533", "A113534", "A113535", "A114045", "A137986", "A137987", "A255321", "A255322", "A255323", "A255344", "A255358", "A255359", "A255360", "A287013", "A348692", "A349079" ]
[ "M2049", "N0811" ]
N. J. A. Sloane
2025-04-22T11:06:41
oeisdata/seq/A000/A000178.seq
5252a43006be98c6ef90defdd1c7478d
A000179
Ménage numbers: a(0) = 1, a(1) = -1, and for n >= 2, a(n) = number of permutations s of [0, ..., n-1] such that s(i) != i and s(i) != i+1 (mod n) for all i.
[ "1", "-1", "0", "1", "2", "13", "80", "579", "4738", "43387", "439792", "4890741", "59216642", "775596313", "10927434464", "164806435783", "2649391469058", "45226435601207", "817056406224416", "15574618910994665", "312400218671253762", "6577618644576902053", "145051250421230224304", "3343382818203784146955", "80399425364623070680706", "2013619745874493923699123" ]
[ "sign", "nice", "easy" ]
263
0
5
[ "A000023", "A000179", "A000186", "A000904", "A008305", "A033999", "A058087", "A059375", "A067998", "A094047", "A102761", "A213234", "A258664", "A258665", "A258666", "A258667", "A258673", "A259212", "A335700" ]
[ "M2062", "N0815" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000179.seq
ccfa0330fda99d83df46f52ca6aab3c3
A000180
Expansion of E.g.f. exp(-x)/(1-3x).
[ "1", "2", "13", "116", "1393", "20894", "376093", "7897952", "189550849", "5117872922", "153536187661", "5066694192812", "182400990941233", "7113638646708086", "298772823161739613", "13444777042278282584", "645349298029357564033", "32912814199497235765682" ]
[ "nonn", "easy" ]
65
0
2
[ "A000180", "A320032" ]
[ "M2063", "N0816" ]
N. J. A. Sloane, Simon Plouffe
2022-05-06T16:34:09
oeisdata/seq/A000/A000180.seq
3899ed9cbd7659268f9f0ecaa4d3eed3
A000181
Coefficients of ménage hit polynomials.
[ "2", "15", "60", "469", "3660", "32958", "328920", "3614490", "43341822", "563144725", "7880897892", "118177520295", "1890389939000", "32130521850972", "578260307815920", "10985555094348948", "219687969344126490", "4613039009310624795", "101479234383619208204", "2333872309936442446905" ]
[ "nonn" ]
27
4
1
[ "A000179", "A000181", "A000425", "A058087" ]
[ "M2076", "N0820" ]
N. J. A. Sloane, Simon Plouffe
2019-06-10T22:59:36
oeisdata/seq/A000/A000181.seq
8e9b9f3de6edf1acf4262d4701e86edb
A000182
Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).
[ "1", "2", "16", "272", "7936", "353792", "22368256", "1903757312", "209865342976", "29088885112832", "4951498053124096", "1015423886506852352", "246921480190207983616", "70251601603943959887872", "23119184187809597841473536", "8713962757125169296170811392", "3729407703720529571097509625856" ]
[ "nonn", "core", "easy", "nice" ]
500
1
2
[ "A000111", "A000182", "A000364", "A001469", "A002105", "A002425", "A002430", "A009006", "A009123", "A009567", "A009725", "A009764", "A012509", "A019538", "A024283", "A029584", "A036279", "A059419", "A064190", "A080635", "A101921", "A110501", "A162005", "A234797", "A258880", "A258901", "A350972" ]
[ "M2096", "N0829" ]
N. J. A. Sloane
2025-03-10T11:12:56
oeisdata/seq/A000/A000182.seq
7541b8b537959e58a7a3ee0d41461b58
A000183
Number of discordant permutations of length n.
[ "0", "0", "0", "1", "2", "20", "144", "1265", "12072", "126565", "1445100", "17875140", "238282730", "3407118041", "52034548064", "845569542593", "14570246018686", "265397214435860", "5095853023109484", "102877234050493609", "2178674876680100744", "48296053720501168037", "1118480911876659396600" ]
[ "nonn", "nice", "easy" ]
61
1
5
[ "A000045", "A000183", "A000338", "A000561", "A000565", "A008305", "A061702", "A061703", "A264801" ]
[ "M2121", "N0838" ]
N. J. A. Sloane
2017-10-20T14:33:52
oeisdata/seq/A000/A000183.seq
4fa13d1a0721d84400c3474b9378aef1
A000184
Number of genus 0 rooted maps with 3 faces with n vertices.
[ "2", "22", "164", "1030", "5868", "31388", "160648", "795846", "3845020", "18211380", "84876152", "390331292", "1775032504", "7995075960", "35715205136", "158401506118", "698102372988", "3059470021316", "13341467466520", "57918065919924", "250419305769512", "1078769490401032", "4631680461623664", "19825379450255900", "84622558822506328", "360270317908904328", "1530148541536781488", "6484511936352543096", "27423786092731382000", "115756362341775227888" ]
[ "nonn" ]
51
2
1
[ "A000108", "A000184", "A029887", "A269920", "A270407" ]
[ "M2128", "N0843" ]
N. J. A. Sloane
2025-01-19T00:34:43
oeisdata/seq/A000/A000184.seq
9d6ae8625789ab4cc0ed4f34ab92e065
A000185
Coefficients of ménage hit polynomials.
[ "2", "24", "140", "1232", "11268", "115056", "1284360", "15596208", "204710454", "2888897032", "43625578836", "702025263328", "11993721979336", "216822550325472", "4135337882588880", "82986434235959712", "1747976804189353962", "38559791049947726328", "889047923669760546140" ]
[ "nonn" ]
25
5
1
[ "A000179", "A000185", "A000425", "A058087" ]
[ "M2135", "N0847" ]
N. J. A. Sloane, Simon Plouffe
2019-06-13T19:55:48
oeisdata/seq/A000/A000185.seq
fb8c8c94e3e2032e1218025de8f52834
A000186
Number of 3 X n Latin rectangles in which the first row is in order.
[ "1", "0", "0", "2", "24", "552", "21280", "1073760", "70299264", "5792853248", "587159944704", "71822743499520", "10435273503677440", "1776780700509416448", "350461958856515690496", "79284041282622163140608", "20392765404792755583221760", "5917934230798104348783083520", "1924427226324694427836833857536" ]
[ "nonn", "nice", "easy" ]
101
0
4
[ "A000166", "A000179", "A000186", "A000512", "A170904", "A335700" ]
[ "M2140", "N0851" ]
N. J. A. Sloane
2024-05-19T14:03:15
oeisdata/seq/A000/A000186.seq
9483eb4603a81e560d828955a189d3b6
A000187
Generalized Euler numbers, c(5,n).
[ "2", "30", "3522", "1066590", "604935042", "551609685150", "737740947722562", "1360427147514751710", "3308161927353377294082", "10256718523496425979562270", "39490468691102039103925777602", "184856411587530526077816051412830", "1033888847501229495999134528615701122" ]
[ "nonn", "easy" ]
67
0
1
[ "A000187", "A000192", "A000320", "A000490", "A060096", "A235605", "A349264", "A349265" ]
[ "M2153", "N0858" ]
N. J. A. Sloane
2024-11-17T03:19:01
oeisdata/seq/A000/A000187.seq
0f4681cac2b4e477489f39ae90e6a2e8
A000188
(1) Number of solutions to x^2 == 0 (mod n). (2) Also square root of largest square dividing n. (3) Also max_{ d divides n } gcd(d, n/d).
[ "1", "1", "1", "2", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "1", "4", "1", "3", "1", "2", "1", "1", "1", "2", "5", "1", "3", "2", "1", "1", "1", "4", "1", "1", "1", "6", "1", "1", "1", "2", "1", "1", "1", "2", "3", "1", "1", "4", "7", "5", "1", "2", "1", "3", "1", "2", "1", "1", "1", "2", "1", "1", "3", "8", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "5", "2", "1", "1", "1", "4", "9", "1", "1", "2", "1", "1", "1", "2", "1", "3" ]
[ "nonn", "easy", "nice", "mult" ]
167
1
4
[ "A000188", "A000189", "A000190", "A007913", "A007947", "A008833", "A015052", "A015053", "A019554", "A019555", "A027748", "A046951", "A053150", "A053164", "A053166", "A055210", "A117811", "A120486", "A124010", "A240976" ]
null
N. J. A. Sloane
2025-02-12T10:43:57
oeisdata/seq/A000/A000188.seq
3b6cdc831b04f6e148140488bf3e2e43
A000189
Number of solutions to x^3 == 0 (mod n).
[ "1", "1", "1", "2", "1", "1", "1", "4", "3", "1", "1", "2", "1", "1", "1", "4", "1", "3", "1", "2", "1", "1", "1", "4", "5", "1", "9", "2", "1", "1", "1", "8", "1", "1", "1", "6", "1", "1", "1", "4", "1", "1", "1", "2", "3", "1", "1", "4", "7", "5", "1", "2", "1", "9", "1", "4", "1", "1", "1", "2", "1", "1", "3", "16", "1", "1", "1", "2", "1", "1", "1", "12", "1", "1", "5", "2", "1", "1", "1", "4", "9", "1", "1", "2", "1", "1", "1", "4", "1", "3" ]
[ "nonn", "mult", "easy" ]
58
1
4
[ "A000189", "A000578", "A019555" ]
null
N. J. A. Sloane
2023-09-09T11:33:37
oeisdata/seq/A000/A000189.seq
eeaa11f9f5bad583107c81749a741634
A000190
Number of solutions to x^4 == 0 (mod n).
[ "1", "1", "1", "2", "1", "1", "1", "4", "3", "1", "1", "2", "1", "1", "1", "8", "1", "3", "1", "2", "1", "1", "1", "4", "5", "1", "9", "2", "1", "1", "1", "8", "1", "1", "1", "6", "1", "1", "1", "4", "1", "1", "1", "2", "3", "1", "1", "8", "7", "5", "1", "2", "1", "9", "1", "4", "1", "1", "1", "2", "1", "1", "3", "16", "1", "1", "1", "2", "1", "1", "1", "12", "1", "1", "5", "2", "1", "1", "1", "8", "27", "1", "1", "2", "1", "1", "1", "4", "1", "3" ]
[ "nonn", "mult", "easy" ]
39
1
4
[ "A000190", "A000583" ]
null
N. J. A. Sloane
2023-12-18T01:45:57
oeisdata/seq/A000/A000190.seq
12feaa0281ddf3a37ce1c542068a0915
A000191
Generalized tangent numbers d(3, n).
[ "2", "46", "3362", "515086", "135274562", "54276473326", "30884386347362", "23657073914466766", "23471059057478981762", "29279357851856595135406", "44855282210826271011257762", "82787899853638102222862479246", "181184428895772987376073015175362", "463938847087789978515380344866258286" ]
[ "nonn", "easy" ]
73
0
1
[ "A000187", "A000191", "A000192", "A000436", "A002437", "A002439", "A007289", "A156172", "A235606", "A349264" ]
[ "M2166", "N0864" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000191.seq
810efe8e5abd58ce772b28deab41a00a
A000192
Generalized Euler numbers c(6,n).
[ "2", "46", "7970", "3487246", "2849229890", "3741386059246", "7205584123783010", "19133892392367261646", "67000387673723462963330", "299131045427247559446422446", "1658470810032820740402966226850", "11179247066648898992009055586869646", "90035623994788132387893239340761189570" ]
[ "nonn", "easy" ]
55
0
1
[ "A000187", "A000191", "A000192", "A000411", "A001587", "A235605", "A349264" ]
[ "M2167", "N0865" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000192.seq
b8347c7176a7261efa409c1b51d082d1
A000193
Nearest integer to log n.
[ "0", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4" ]
[ "nonn", "easy" ]
19
1
5
[ "A000193", "A000195", "A004233" ]
null
N. J. A. Sloane
2024-06-28T05:26:18
oeisdata/seq/A000/A000193.seq
ba317f0e39a4e9f67bbd7cb2c8bd9af7
A000194
n appears 2n times, for n >= 1; also nearest integer to square root of n.
[ "0", "1", "1", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "10", "10", "10" ]
[ "nonn", "easy", "nice" ]
131
0
4
[ "A000037", "A000194", "A000196", "A002024", "A002061", "A002378", "A003059", "A005369", "A053187", "A105209", "A259351" ]
null
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000194.seq
8514b62e1b4632697581738d2121c753
A000195
a(n) = floor(log(n)).
[ "0", "0", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4" ]
[ "nonn", "easy" ]
40
1
8
[ "A000193", "A000195", "A000523", "A004233" ]
null
N. J. A. Sloane
2024-08-28T04:25:28
oeisdata/seq/A000/A000195.seq
c57e742e60eec9783a3f7f317c7631f0
A000196
Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times.
[ "0", "1", "1", "1", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10" ]
[ "nonn", "easy", "nice" ]
198
0
5
[ "A000196", "A000290", "A002162", "A003056", "A028391", "A048760", "A048766", "A074704", "A079051", "A281871" ]
null
N. J. A. Sloane
2024-06-25T08:32:45
oeisdata/seq/A000/A000196.seq
6bf4f019fdfc9e815236ba14ac4d7b2b
A000197
a(n) = (n!)!.
[ "1", "1", "2", "720", "620448401733239439360000" ]
[ "nonn", "easy" ]
52
0
3
[ "A000142", "A000197", "A006990", "A063979", "A152168", "A245087" ]
[ "M2187", "N0874" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000197.seq
cdfc8bf3a667e461a139d409a18f6e33
A000198
Largest order of automorphism group of a tournament with n nodes.
[ "1", "1", "3", "3", "5", "9", "21", "21", "81", "81", "81", "243", "243", "441", "1215", "1701", "1701", "6561", "6561", "6561", "45927", "45927", "45927", "137781", "137781", "229635", "1594323", "1594323", "1594323", "4782969", "4782969", "7971615", "14348907", "33480783", "33480783", "129140163", "129140163", "129140163" ]
[ "nonn", "nice" ]
59
1
3
[ "A000198", "A000568", "A374164" ]
[ "M2280", "N0902" ]
N. J. A. Sloane
2024-07-01T14:55:37
oeisdata/seq/A000/A000198.seq
a1052cb6ef2f867ecb990193cb1fbcd5
A000199
Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
[ "1", "3", "3", "7", "6", "12", "13", "20", "21", "34", "36", "51", "58", "78", "89", "118", "131", "171", "197", "245", "279", "349", "398", "486", "557", "671", "767", "920", "1046", "1244", "1421", "1667", "1898", "2225", "2525", "2937", "3333", "3856", "4367", "5034", "5683", "6521", "7365", "8409", "9473", "10795", "12133", "13775", "15466" ]
[ "nonn" ]
31
1
2
[ "A000025", "A000039", "A000199" ]
[ "M2285", "N0904" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000199.seq
dad4862924e542a1e08031a26ab8a629
A000200
Number of bicentered hydrocarbons with n atoms.
[ "0", "0", "1", "0", "1", "1", "3", "3", "9", "15", "38", "73", "174", "380", "915", "2124", "5134", "12281", "30010", "73401", "181835", "452165", "1133252", "2851710", "7215262", "18326528", "46750268", "119687146", "307528889", "792716193", "2049703887", "5314775856", "13817638615", "36012395538" ]
[ "nonn", "nice" ]
40
0
7
[ "A000022", "A000200", "A000602", "A010373" ]
[ "M2288", "N0905" ]
N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)
2020-12-19T03:13:09
oeisdata/seq/A000/A000200.seq
30a966402842105d0ee0fb4af8efc463