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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A002601
A generalized partition function.
[ "1", "10", "34", "58", "73", "79", "86", "152", "265", "457", "763", "1268", "2058", "3308", "5236", "8220", "12731", "19546", "29685", "44702", "66714", "98806", "145154", "211756", "306667", "441249", "630771", "896344", "1266146", "1778692", "2485086", "3454206", "4777165", "6575350", "9008159" ]
[ "nonn" ]
26
1
2
null
[ "M4694", "N2004" ]
N. J. A. Sloane
2023-10-17T08:18:55
oeisdata/seq/A002/A002601.seq
86d6901a28a8d1b107471c66e743e8fb
A002602
A generalized partition function.
[ "1", "15", "51", "97", "127", "145", "152", "160", "273", "481", "811", "1372", "2250", "3692", "5924", "9472", "14887", "23310", "36005", "55314", "84042", "126998", "190138", "283108", "418175", "614429", "896439", "1301168", "1876826", "2693988", "3845134", "5462744", "7720947", "10864828", "15216527" ]
[ "nonn" ]
23
1
2
null
[ "M4965", "N2130" ]
N. J. A. Sloane
2023-10-17T08:19:00
oeisdata/seq/A002/A002602.seq
7e78e9565a8ac1509a45701ba16c1b69
A002603
A generalized partition function.
[ "1", "15", "73", "143", "208", "244", "265", "273", "282", "490", "838", "1426", "2367", "3908", "6356", "10246", "16327", "25812", "40379", "62748", "96660", "147833", "224446", "338584", "507293", "755612", "1118679", "1647023", "2411642", "3513096", "5091511", "7344086", "10543419", "15068833", "21442703", "30385111", "42880601" ]
[ "nonn" ]
21
1
2
null
[ "M4971", "N2134" ]
N. J. A. Sloane
2023-10-17T08:19:05
oeisdata/seq/A002/A002603.seq
3a4fdd1f9827f01440a55d9e048e3423
A002604
a(n) = n^6 + 1.
[ "1", "2", "65", "730", "4097", "15626", "46657", "117650", "262145", "531442", "1000001", "1771562", "2985985", "4826810", "7529537", "11390626", "16777217", "24137570", "34012225", "47045882", "64000001", "85766122", "113379905", "148035890" ]
[ "nonn", "easy" ]
31
0
2
[ "A001014", "A002522", "A002604", "A024004" ]
null
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002604.seq
0c3cf647eb06b49bc65573f97176e600
A002605
a(n) = 2*(a(n-1) + a(n-2)), a(0) = 0, a(1) = 1.
[ "0", "1", "2", "6", "16", "44", "120", "328", "896", "2448", "6688", "18272", "49920", "136384", "372608", "1017984", "2781184", "7598336", "20759040", "56714752", "154947584", "423324672", "1156544512", "3159738368", "8632565760", "23584608256", "64434348032", "176037912576", "480944521216", "1313964867584" ]
[ "nonn", "easy", "changed" ]
269
0
3
[ "A000129", "A001333", "A002530", "A002532", "A002533", "A002605", "A015518", "A015519", "A026150", "A028859", "A028860", "A030195", "A046717", "A052948", "A063727", "A073387", "A077846", "A077917", "A080040", "A080953", "A081577", "A083098", "A083099", "A083100", "A083337", "A084057", "A106435", "A108898", "A125145", "A156710", "A175289", "A265106", "A265107", "A265278", "A270810", "A293005", "A293006", "A293007" ]
null
Colin Mallows
2025-04-18T13:02:13
oeisdata/seq/A002/A002605.seq
6173fd106ea5a2d2d23282b70594c6aa
A002606
Weight distribution of Karlin's [28,14,8] double circulant code.
[ "1", "0", "0", "0", "546", "1456", "3549", "5280", "3549", "1456", "546", "0", "0", "0", "1" ]
[ "nonn", "fini", "full" ]
9
0
5
null
null
N. J. A. Sloane
2023-10-17T07:11:26
oeisdata/seq/A002/A002606.seq
2025c96a6972699c7fef578b01934666
A002607
Glaisher's chi_8(n).
[ "1", "16", "0", "256", "-1054", "0", "0", "4096", "6561", "-16864", "0", "0", "-478", "0", "0", "65536", "-63358", "104976", "0", "-269824", "0", "0", "0", "0", "720291", "-7648", "0", "0", "-1407838", "0", "0", "1048576", "0", "-1013728", "0", "1679616", "925922", "0", "0", "-4317184", "3577922", "0", "0", "0", "-6915294", "0", "0", "0", "5764801", "11524656", "0", "-122368" ]
[ "sign", "mult" ]
58
1
2
[ "A002607", "A030212", "A247067" ]
[ "M4994", "N2150" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002607.seq
09feab885895eda02f7242173e367683
A002608
Glaisher's function T(2n+1).
[ "33", "524", "-2322", "81912", "214181", "1182276", "3736614", "9972264", "24622002", "51265020", "106396576", "202547304", "357914103", "613924280", "1011319830", "1625884896", "2508545328", "3777689232", "5589515982", "8076649672", "11456490906", "15968552484", "22005025446" ]
[ "sign" ]
25
0
1
[ "A002607", "A002608" ]
[ "M5242", "N2281" ]
N. J. A. Sloane
2019-03-04T01:54:17
oeisdata/seq/A002/A002608.seq
03db5eeb5add771a498352bb55e7e67c
A002609
Glaisher's function G(n) (18 squares version).
[ "1", "-20", "-80", "144", "610", "-448", "-1120", "2240", "-3423", "-12200", "14800", "29440", "-5470", "-6272", "-48800", "-81664", "73090", "68460", "15600", "87840", "-139776", "82880", "189920", "-474112", "-18525", "109400", "-251040", "412160", "-128222", "-273280", "54400", "1059840", "1847040" ]
[ "sign" ]
25
1
2
[ "A002111", "A002609" ]
[ "M5088", "N2203" ]
N. J. A. Sloane
2023-10-17T07:17:57
oeisdata/seq/A002/A002609.seq
21e81f0782749dcbaf82a4a3ddd5c870
A002610
Glaisher's function H'(4n+1) (18 squares version).
[ "0", "1", "-6", "-3", "82", "-84", "-444", "769", "1110", "-2643", "-860", "2901", "-1176", "6277", "1170", "-21315", "-2308", "14244", "29442", "15540", "-58194", "-13338", "-31886", "4080", "176682", "-70715", "-51240", "81489", "-135728", "13137", "-205350", "58826", "355974", "16380", "530932", "-457944", "-938748", "140329", "99462", "317157" ]
[ "sign" ]
30
0
3
[ "A002288", "A002610" ]
[ "M4051", "N1681" ]
N. J. A. Sloane
2019-03-04T06:07:39
oeisdata/seq/A002/A002610.seq
175f198f94deb21baa5353b5ec8fd4a0
A002611
Glaisher's function V(n).
[ "0", "1", "4", "-4", "-32", "-16", "56", "80", "192", "98", "-740", "-704", "96", "-224", "2440", "3520", "-2624", "-351", "-780", "-10632", "2688", "2960", "-9496", "18176", "14208", "-3934", "12552", "-9856", "-24608", "-9760", "-2720", "-25344", "-35520", "31106", "34160", "62844", "84576", "3120", "-21880", "-82272", "27520", "-96768", "-237316", "130240", "-92832", "37984", "305296", "-183296", "37632", "208803" ]
[ "sign" ]
20
1
3
[ "A002288", "A002611", "A004018" ]
[ "M3235", "N1305" ]
N. J. A. Sloane
2019-03-04T01:53:55
oeisdata/seq/A002/A002611.seq
840a0d548a5a45def6d6cf7dcd016493
A002612
Glaisher's function U(n).
[ "1", "12", "48", "16", "-414", "-960", "672", "4800", "2721", "-9064", "-8880", "6912", "-2398", "-13440", "29280", "30976", "-10878", "57228", "-9360", "-252384", "-53760", "177600", "-113952", "107520", "436131", "-16488", "150624", "96768", "-915678", "-585600", "-32640", "248832", "710400", "-466408" ]
[ "sign" ]
23
1
2
null
[ "M4836", "N2067" ]
N. J. A. Sloane
2023-10-17T07:18:10
oeisdata/seq/A002/A002612.seq
25a0e7f85e26761bda34c3abb48d9bfe
A002613
Glaisher's function J(n) (18 squares version).
[ "1", "44", "432", "-1136", "610", "-5568", "6048", "11456", "-3423", "26840", "-79920", "768", "-5470", "-77952", "263520", "61696", "73090", "-150612", "-84240", "-692960", "-139776", "1030080", "-1025568", "1410048", "-18525", "-240680", "1355616", "10752", "-128222", "-3396480", "-293760" ]
[ "sign" ]
25
1
2
[ "A002609", "A002613" ]
[ "M5284", "N2300" ]
N. J. A. Sloane
2023-10-17T07:17:22
oeisdata/seq/A002/A002613.seq
be61bb739307a46badd5d6d3720117cb
A002614
Glaisher's function theta(n) (18 squares version).
[ "0", "-7", "128", "-975", "4608", "-16340", "48384", "-124303", "281600", "-583746", "1146240", "-2125108", "3691008", "-6151880", "10055424", "-15914895", "24136704", "-35748899", "52583040", "-75877938", "105994240", "-145580124", "200279808", "-272040500", "359036928", "-468767690", "615599360" ]
[ "sign" ]
23
1
2
[ "A002288", "A002614", "A321546" ]
[ "M4459", "N1890" ]
N. J. A. Sloane
2023-10-17T07:19:41
oeisdata/seq/A002/A002614.seq
6a0a009a953c154c462c45fe8e9c9997
A002615
Glaisher's function T_1(n).
[ "19", "-145", "100", "2191", "-8598", "14516", "-29080", "114575", "-320417", "615666", "-1125492", "2139700", "-3664750", "5997448", "-10103304", "15992719", "-23857290", "36059435", "-53341900", "75622578", "-105762592", "145414140", "-198974280", "271923764", "-359683403", "468557626" ]
[ "sign" ]
29
1
1
[ "A002288", "A002614", "A002615" ]
[ "M5076", "N2196" ]
N. J. A. Sloane
2019-03-04T17:10:48
oeisdata/seq/A002/A002615.seq
e3c8bbfa1dc4b8be8a53ddcbcb5412fd
A002616
Reduced totient function (divided by 2).
[ "1", "1", "2", "1", "3", "1", "3", "2", "5", "1", "6", "3", "2", "2", "8", "3", "9", "2", "3", "5", "11", "1", "10", "6", "9", "3", "14", "2", "15", "4", "5", "8", "6", "3", "18", "9", "6", "2", "20", "3", "21", "5", "6", "11", "23", "2", "21", "10", "8", "6", "26", "9", "10", "3", "9", "14", "29", "2", "30", "15", "3", "8", "6", "5", "33", "8", "11", "6", "35", "3", "36", "18", "10", "9", "15", "6", "39", "2", "27", "20", "41", "3", "8", "21", "14", "5", "44", "6", "6" ]
[ "nonn", "easy" ]
31
3
3
[ "A002322", "A002616" ]
[ "M0128", "N0052" ]
N. J. A. Sloane
2022-05-22T04:12:48
oeisdata/seq/A002/A002616.seq
769f0c8861435d8d7cdd21145a5d5d41
A002617
Weight distribution of Cheng-Sloane [ 32,17,8 ] code.
[ "1", "0", "0", "0", "908", "3328", "14784", "27392", "38246", "27392", "14784", "3328", "908", "0", "0", "0", "1" ]
[ "nonn", "fini", "full" ]
11
0
5
null
null
N. J. A. Sloane
2023-10-17T07:20:44
oeisdata/seq/A002/A002617.seq
f7e37099d5ee6f8c3bdbc5c3bf7a6c0f
A002618
a(n) = n*phi(n).
[ "1", "2", "6", "8", "20", "12", "42", "32", "54", "40", "110", "48", "156", "84", "120", "128", "272", "108", "342", "160", "252", "220", "506", "192", "500", "312", "486", "336", "812", "240", "930", "512", "660", "544", "840", "432", "1332", "684", "936", "640", "1640", "504", "1806", "880", "1080", "1012", "2162", "768", "2058", "1000" ]
[ "nonn", "easy", "nice", "mult", "look" ]
201
1
2
[ "A000010", "A002618", "A002619", "A009262", "A011755", "A036689", "A047916", "A047918", "A053191", "A053192", "A053650", "A058161", "A065484", "A082473", "A256545", "A323333", "A327172", "A327173" ]
[ "M1568", "N0611" ]
N. J. A. Sloane
2024-10-26T06:26:48
oeisdata/seq/A002/A002618.seq
22f6a24d62736051bb68f10c8b3fb4dd
A002619
Number of 2-colored patterns on an n X n board.
[ "1", "1", "2", "3", "8", "24", "108", "640", "4492", "36336", "329900", "3326788", "36846288", "444790512", "5811886656", "81729688428", "1230752346368", "19760413251956", "336967037143596", "6082255029733168", "115852476579940152", "2322315553428424200", "48869596859895986108" ]
[ "nonn", "nice", "easy" ]
88
1
3
[ "A000010", "A000939", "A000940", "A002618", "A002619", "A047916", "A064649", "A064852", "A089066", "A262480", "A275527" ]
[ "M0887", "N0336" ]
N. J. A. Sloane, Colin Mallows
2022-11-07T13:45:57
oeisdata/seq/A002/A002619.seq
6ad1c313e1f0a587109e3e4d965c741c
A002620
Quarter-squares: a(n) = floor(n/2)*ceiling(n/2). Equivalently, a(n) = floor(n^2/4).
[ "0", "0", "1", "2", "4", "6", "9", "12", "16", "20", "25", "30", "36", "42", "49", "56", "64", "72", "81", "90", "100", "110", "121", "132", "144", "156", "169", "182", "196", "210", "225", "240", "256", "272", "289", "306", "324", "342", "361", "380", "400", "420", "441", "462", "484", "506", "529", "552", "576", "600", "625", "650", "676", "702", "729", "756", "784", "812" ]
[ "nonn", "easy", "nice", "core", "changed" ]
824
0
4
[ "A000212", "A000290", "A000601", "A002620", "A002623", "A002984", "A003983", "A004526", "A005044", "A006501", "A007590", "A008217", "A008233", "A008382", "A008881", "A009641", "A009694", "A009714", "A014616", "A014980", "A024206", "A030179", "A030511", "A033436", "A033437", "A033438", "A033439", "A033444", "A033638", "A049068", "A055802", "A055803", "A056827", "A056834", "A056838", "A056865", "A060656", "A063657", "A072280", "A077043", "A078126", "A087811", "A115514", "A118013", "A118015", "A128174", "A130519", "A171608", "A176222", "A184535", "A189151", "A197081", "A197122", "A250000", "A275437", "A344678", "A354600", "A355509" ]
[ "M0998", "N0374" ]
N. J. A. Sloane
2025-04-18T03:19:00
oeisdata/seq/A002/A002620.seq
4e0a7af8290bd8a8594cf8cce6d9f379
A002621
Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
[ "1", "2", "4", "7", "12", "18", "27", "38", "53", "71", "94", "121", "155", "194", "241", "295", "359", "431", "515", "609", "717", "837", "973", "1123", "1292", "1477", "1683", "1908", "2157", "2427", "2724", "3045", "3396", "3774", "4185", "4626", "5104", "5615", "6166", "6754", "7386", "8058", "8778", "9542", "10358", "11222", "12142", "13114" ]
[ "nonn", "easy" ]
70
0
2
[ "A001400", "A002621", "A092905" ]
[ "M1051", "N0394" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A002/A002621.seq
cb0c0eb77483faf60e7afded00fdf748
A002622
Number of partitions of at most n into at most 5 parts.
[ "1", "2", "4", "7", "12", "19", "29", "42", "60", "83", "113", "150", "197", "254", "324", "408", "509", "628", "769", "933", "1125", "1346", "1601", "1892", "2225", "2602", "3029", "3509", "4049", "4652", "5326", "6074", "6905", "7823", "8837", "9952", "11178", "12520", "13989", "15591", "17338", "19236", "21298", "23531", "25949", "28560", "31378", "34412" ]
[ "nonn", "easy" ]
64
0
2
[ "A001401", "A002622", "A092905" ]
[ "M1053", "N0395" ]
N. J. A. Sloane
2020-08-19T15:43:16
oeisdata/seq/A002/A002622.seq
1f4a217daeb4172ad512eb2cd9a84829
A002623
Expansion of 1/((1-x)^4*(1+x)).
[ "1", "3", "7", "13", "22", "34", "50", "70", "95", "125", "161", "203", "252", "308", "372", "444", "525", "615", "715", "825", "946", "1078", "1222", "1378", "1547", "1729", "1925", "2135", "2360", "2600", "2856", "3128", "3417", "3723", "4047", "4389", "4750", "5130", "5530", "5950", "6391", "6853", "7337", "7843", "8372", "8924", "9500" ]
[ "nonn", "easy", "nice" ]
297
0
2
[ "A000217", "A000292", "A001752", "A002412", "A002620", "A002623", "A002717", "A002727", "A006148", "A006918", "A014125", "A016061", "A057524", "A058187", "A062109", "A108561", "A122046", "A122047", "A134446", "A175724" ]
[ "M2640", "N1050" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002623.seq
d2df8ec48a75dc0faabdc2293966662b
A002624
Expansion of (1-x)^(-3) * (1-x^2)^(-2).
[ "1", "3", "8", "16", "30", "50", "80", "120", "175", "245", "336", "448", "588", "756", "960", "1200", "1485", "1815", "2200", "2640", "3146", "3718", "4368", "5096", "5915", "6825", "7840", "8960", "10200", "11560", "13056", "14688", "16473", "18411", "20520", "22800", "25270", "27930", "30800", "33880", "37191", "40733", "44528" ]
[ "nonn", "easy" ]
127
0
2
[ "A002624", "A047659", "A139600", "A180662" ]
[ "M2723", "N1091" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A002/A002624.seq
9bdd2b2aa03d4a5f3fc4a355cc1a365c
A002625
Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
[ "1", "3", "8", "17", "33", "58", "97", "153", "233", "342", "489", "681", "930", "1245", "1641", "2130", "2730", "3456", "4330", "5370", "6602", "8048", "9738", "11698", "13963", "16563", "19538", "22923", "26763", "31098", "35979", "41451", "47571", "54390", "61971", "70371", "79660", "89901", "101171", "113540", "127092", "141904", "158068", "175668", "194804", "215568" ]
[ "nonn", "easy" ]
54
0
2
[ "A002625", "A097701" ]
[ "M2726", "N1093" ]
N. J. A. Sloane
2022-09-24T13:44:32
oeisdata/seq/A002/A002625.seq
4964ced1381887a883674d0cef432248
A002626
Expansion of 1/((1-x)^3 (1-x^2)^2 (1-x^3) (1-x^4)).
[ "1", "3", "8", "17", "34", "61", "105", "170", "267", "403", "594", "851", "1197", "1648", "2235", "2981", "3927", "5104", "6565", "8351", "10529", "13152", "16303", "20049", "24492", "29715", "35841", "42972", "51255", "60813", "71820", "84423", "98826", "115203", "133791", "154794", "178486", "205104", "234962", "268334", "305578" ]
[ "nonn", "easy" ]
35
0
2
null
[ "M2727", "N1094" ]
N. J. A. Sloane
2023-10-17T07:22:10
oeisdata/seq/A002/A002626.seq
31f439f60e55313c98e06dd3556c2c8b
A002627
a(n) = n*a(n-1) + 1, a(0) = 0.
[ "0", "1", "3", "10", "41", "206", "1237", "8660", "69281", "623530", "6235301", "68588312", "823059745", "10699776686", "149796873605", "2246953104076", "35951249665217", "611171244308690", "11001082397556421", "209020565553572000", "4180411311071440001", "87788637532500240022" ]
[ "nonn", "easy", "nice" ]
175
0
3
[ "A000522", "A001113", "A002627", "A056542", "A059922", "A092582", "A130147" ]
[ "M2858", "N1149" ]
N. J. A. Sloane
2024-05-20T13:50:17
oeisdata/seq/A002/A002627.seq
62bec6cdad362dfba1eb3078e89adffb
A002628
Number of permutations of length n without 3-sequences.
[ "1", "1", "2", "5", "21", "106", "643", "4547", "36696", "332769", "3349507", "37054436", "446867351", "5834728509", "82003113550", "1234297698757", "19809901558841", "337707109446702", "6094059760690035", "116052543892621951", "2325905946434516516", "48937614361477154273", "1078523843237914046247" ]
[ "nonn" ]
40
0
3
[ "A000166", "A002628", "A047921", "A165960", "A165961", "A165962", "A180185" ]
[ "M1536", "N0600" ]
N. J. A. Sloane
2021-04-20T12:58:35
oeisdata/seq/A002/A002628.seq
9a3bf1413c5fd0e1af8a641bde348e00
A002629
Number of permutations of length n with one 3-sequence.
[ "0", "0", "1", "2", "11", "62", "406", "3046", "25737", "242094", "2510733", "28473604", "350651588", "4661105036", "66529260545", "1014985068610", "16484495344135", "283989434253186", "5173041992087562", "99346991708245506", "2006304350543326057", "42505510227603678206", "942678881135812883321" ]
[ "nonn" ]
32
1
4
[ "A000166", "A002629", "A047921" ]
[ "M2003", "N0792" ]
N. J. A. Sloane
2021-12-19T10:08:13
oeisdata/seq/A002/A002629.seq
e4df672aeec8ccfc4756435d8f8dcc60
A002630
Number of permutations of length n with two 3-sequences.
[ "0", "0", "0", "1", "2", "12", "71", "481", "3708", "32028", "306723", "3228804", "37080394", "461569226", "6192527700", "89102492915", "1369014167140", "22373840093040", "387602212164321", "7095737193164187", "136885937242792752", "2775675888994318366", "59023506305591628101", "1313445236142071926488" ]
[ "nonn" ]
25
1
5
[ "A002630", "A047921" ]
[ "M2032", "N0804" ]
N. J. A. Sloane
2024-05-06T08:23:22
oeisdata/seq/A002/A002630.seq
d404f5f435dcda47ac4619ab50a2944e
A002631
Number of circuits of nullity n.
[ "1", "2", "5", "16", "67", "435" ]
[ "nonn", "more", "nice" ]
14
1
2
[ "A002631", "A002632" ]
[ "M1502", "N0590" ]
N. J. A. Sloane
2015-11-25T01:51:43
oeisdata/seq/A002/A002631.seq
b820576e214dd36dad06d95ed97b0a45
A002632
Erroneous version of A377569.
[ "1", "2", "5", "16", "73", "538" ]
[ "dead" ]
19
1
2
null
[ "M1503", "N0591" ]
N. J. A. Sloane
2024-11-01T23:44:01
oeisdata/seq/A002/A002632.seq
e8bfbe81493b5b47c03d0d5f318a285a
A002633
Related to discordant permutations.
[ "1", "-3", "5", "-3", "9", "-3", "-51", "-675", "-5871", "-46467", "-331371", "-1852227", "-920295", "224455293", "5571057501", "104877816093", "1781775072801", "28519837563645", "431525731169061", "5994769814117757", "68879336771960361", "346333945918252797", "-15047168730918615315", "-793523760950138583843" ]
[ "sign", "easy" ]
37
0
2
[ "A002633", "A213170", "A269953" ]
[ "M2384", "N0946" ]
N. J. A. Sloane
2024-07-31T09:49:26
oeisdata/seq/A002/A002633.seq
3097bab5e01a2042b5e3c416df2a5f92
A002634
From discordant permutations.
[ "-2", "3", "0", "25", "152", "1350", "12644", "131391", "1489568", "18329481", "243365514", "3468969962", "52848096274", "857073295427", "14744289690560", "268202790690465", "5143861702523924", "103746422699053582", "2195275169113687656", "48629604864202585247" ]
[ "sign" ]
22
3
1
[ "A000183", "A002634" ]
[ "M0397", "N0153" ]
N. J. A. Sloane
2018-01-11T01:09:03
oeisdata/seq/A002/A002634.seq
1e507e0d98b0e8c7bd2b2d8ed4219eb6
A002635
Number of partitions of n into 4 squares.
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "2", "3", "2", "2", "2", "2", "1", "1", "3", "3", "3", "3", "2", "2", "2", "1", "3", "4", "2", "4", "3", "3", "2", "2", "3", "4", "3", "2", "4", "2", "2", "2", "4", "5", "3", "5", "3", "5", "3", "1", "4", "5", "3", "3", "4", "3", "4", "2", "4", "6", "4", "4", "4", "5", "2", "3", "5", "5", "5", "5", "4", "4", "3", "2", "6", "7", "4", "5", "5", "5", "4", "2", "5", "9", "5", "3", "5", "4", "3", "1", "6", "7", "6", "7", "5", "7", "5", "3", "6", "7", "4" ]
[ "nonn", "easy", "nice" ]
37
0
5
[ "A000161", "A000164", "A000174", "A000177", "A000290", "A002635", "A006431", "A010052", "A025422", "A025423", "A025424", "A025425", "A124978", "A180149", "A245022" ]
[ "M0053", "N0018" ]
N. J. A. Sloane
2022-01-29T01:03:15
oeisdata/seq/A002/A002635.seq
3707fd6133414965de565c009b794997
A002636
Number of ways of writing n as an unordered sum of at most 3 nonzero triangular numbers.
[ "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "3", "2", "1", "2", "3", "2", "2", "2", "1", "4", "3", "2", "2", "2", "2", "3", "3", "1", "4", "4", "2", "2", "3", "2", "3", "4", "2", "3", "3", "2", "4", "3", "2", "4", "4", "2", "4", "4", "1", "4", "5", "1", "2", "3", "4", "6", "4", "3", "2", "5", "2", "3", "3", "3", "6", "5", "2", "2", "5", "3", "5", "4", "2", "4", "5", "3", "4", "5", "2", "4", "6", "2", "6", "3", "3", "6", "3", "2", "3", "7", "3", "6", "6", "2", "4", "6", "3", "2" ]
[ "nonn", "easy", "nice" ]
41
0
4
[ "A002636", "A007294", "A008443", "A053604", "A061262", "A063993" ]
[ "M0076", "N0027" ]
N. J. A. Sloane, Sep 18 2001
2021-03-29T16:49:05
oeisdata/seq/A002/A002636.seq
34ea021c754b2073fcc15df5fe18f909
A002637
Number of partitions of n into not more than 5 pentagonal numbers.
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "2", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "3", "3", "2", "3", "2", "2", "2", "1", "2", "1", "3", "3", "3", "4", "3", "3", "2", "3", "3", "1", "2", "3", "4", "4", "3", "4", "3", "4", "3", "3", "3", "3", "3", "4", "5", "5", "3", "3", "4", "4", "3", "2", "4", "3", "4", "4", "5", "6", "5", "5", "4", "5", "6", "3", "4", "4", "6", "5", "4", "5", "4", "6", "4", "5", "6", "4", "3", "3", "8", "7", "5", "6", "5", "7", "5", "6", "5", "3", "6", "5", "7", "7" ]
[ "nonn", "easy" ]
30
1
5
null
[ "M0050", "N0016" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002637.seq
ad1af153bc3c0a68e0479e5a9bc973d7
A002638
a(n) = (number of nonisomorphic nontransitive prime tournaments on n nodes) - Moebius(n).
[ "-1", "1", "2", "3", "12", "52", "456", "6873", "191532", "9733032", "903753248", "154108311046", "48542114686912", "28401423719121392", "31021002160355166800", "63530415842308265086523", "244912778438520759443245824", "1783398846284777975419599903948", "24605641171260376770598003978281472" ]
[ "sign" ]
39
1
3
[ "A000568", "A002638", "A008683", "A259106" ]
[ "M0913", "N0345" ]
N. J. A. Sloane
2024-12-27T22:37:42
oeisdata/seq/A002/A002638.seq
173bdc60c5b433ea28f66b3508fea2cd
A002639
Numerators of expansion of Jacobi nome q in parameter m.
[ "0", "1", "1", "21", "31", "6257", "10293", "279025", "483127", "435506703", "776957575", "22417045555", "40784671953", "9569130097211", "17652604545791", "523910972020563", "976501268709949", "935823746406530603", "1758220447807291611" ]
[ "nonn", "nice", "frac" ]
50
0
4
[ "A002103", "A002639", "A005797", "A119349" ]
[ "M5108", "N2212" ]
N. J. A. Sloane
2025-03-26T06:41:52
oeisdata/seq/A002/A002639.seq
683bec8e954aa59d90f0833f03111c44
A002640
Numbers k such that (k^2 + k + 1)/3 is prime.
[ "4", "7", "10", "13", "19", "28", "31", "34", "40", "43", "52", "70", "73", "76", "82", "85", "91", "97", "103", "112", "115", "124", "127", "136", "145", "148", "157", "166", "175", "187", "190", "199", "202", "223", "241", "244", "259", "265", "271", "274", "280", "286", "316", "325", "358", "370", "376", "385", "388", "409", "421", "427", "442", "460", "469", "472" ]
[ "nonn", "easy" ]
34
1
1
null
[ "M3301", "N1331" ]
N. J. A. Sloane
2023-10-17T08:19:10
oeisdata/seq/A002/A002640.seq
90485c773a983369bad8230dd1886b0f
A002641
Numbers k such that (k^2 + k + 1)/7 is prime.
[ "4", "9", "11", "23", "32", "39", "44", "51", "53", "60", "65", "72", "86", "93", "95", "114", "123", "156", "170", "179", "186", "200", "207", "212", "219", "228", "233", "240", "249", "261", "270", "303", "317", "333", "338", "345", "375", "389", "401", "443", "452", "473", "480", "492", "515", "534", "548", "564", "578", "585", "597", "599", "611", "641", "660", "662" ]
[ "nonn", "easy" ]
35
1
1
[ "A002641", "A047348" ]
[ "M3352", "N0446" ]
N. J. A. Sloane
2022-02-26T14:42:28
oeisdata/seq/A002/A002641.seq
d9218fd181839823142509fc311dc200
A002642
Numbers k such that (k^2 + k + 1)/13 is prime.
[ "9", "29", "35", "42", "48", "113", "120", "126", "152", "185", "204", "224", "237", "243", "276", "302", "308", "321", "341", "386", "399", "419", "432", "477", "503", "510", "516", "542", "549", "588", "633", "659", "666", "705", "731", "770", "776", "783", "789", "815", "848", "854", "887", "906", "932", "945", "965", "978" ]
[ "nonn", "easy" ]
25
1
1
null
[ "M4606", "N1131" ]
N. J. A. Sloane
2023-10-17T08:19:14
oeisdata/seq/A002/A002642.seq
28ae104973653ec90df319be2c134ecc
A002643
Numbers k such that (k^2 + k + 1)/19 is prime.
[ "7", "11", "26", "45", "83", "125", "140", "182", "197", "201", "216", "239", "258", "311", "330", "353", "444", "467", "482", "486", "524", "539", "558", "600", "752", "771", "843", "881", "885", "923", "980", "999", "1071", "1113", "1170", "1223", "1337", "1356", "1470", "1664", "1835", "1869", "1911", "1949", "1968", "2021", "2078", "2120", "2192" ]
[ "nonn", "easy" ]
33
1
1
[ "A002640", "A002641", "A002642", "A002643", "A002644" ]
[ "M4340", "N1817" ]
N. J. A. Sloane
2024-07-31T09:50:22
oeisdata/seq/A002/A002643.seq
64f5deb222aa2bc75b35177eeb62f4f6
A002644
Numbers k such that (k^2 + k + 1)/21 is prime.
[ "16", "25", "37", "46", "58", "88", "109", "130", "142", "151", "184", "193", "205", "247", "268", "298", "310", "319", "331", "340", "382", "394", "403", "415", "424", "457", "478", "487", "541", "550", "604", "613", "688", "697", "709", "730", "739", "751", "760", "793", "844", "865", "886", "907", "970", "1012", "1045", "1054", "1066", "1117", "1138" ]
[ "nonn", "easy" ]
27
1
1
null
[ "M5000", "N1426" ]
N. J. A. Sloane
2023-10-18T10:04:17
oeisdata/seq/A002/A002644.seq
a3da4bb075b9f367fb3d1a554975662d
A002645
Quartan primes: primes of the form x^4 + y^4, x > 0, y > 0.
[ "2", "17", "97", "257", "337", "641", "881", "1297", "2417", "2657", "3697", "4177", "4721", "6577", "10657", "12401", "14657", "14897", "15937", "16561", "28817", "38561", "39041", "49297", "54721", "65537", "65617", "66161", "66977", "80177", "83537", "83777", "89041", "105601", "107377", "119617", "121937" ]
[ "nonn", "easy" ]
84
1
1
[ "A000040", "A000290", "A000583", "A002313", "A002645", "A002646", "A003336", "A004831", "A028916", "A256852" ]
[ "M5042", "N2178" ]
N. J. A. Sloane
2023-10-28T12:22:15
oeisdata/seq/A002/A002645.seq
81299ddd3d73f7d15a8cffec82c0c7bb
A002646
Half-quartan primes: primes of the form p = (x^4 + y^4)/2.
[ "41", "313", "353", "1201", "3593", "4481", "7321", "8521", "10601", "14281", "14321", "14593", "21601", "26513", "32633", "41761", "41801", "42073", "42961", "49081", "56041", "66361", "67073", "72481", "90473", "97241", "97553", "104561", "106921", "111521", "139921", "141121", "165233", "195353", "198593" ]
[ "nonn", "nice" ]
77
1
1
[ "A000583", "A002645", "A002646", "A005408", "A010051" ]
[ "M5276", "N2294" ]
N. J. A. Sloane
2023-09-02T18:05:27
oeisdata/seq/A002/A002646.seq
0fb506ee6e6e905d9e29c845a7a0dda5
A002647
Sextan primes: p = (x^6 + y^6)/(x^2 + y^2).
[ "13", "61", "73", "193", "241", "541", "601", "1021", "1801", "1873", "1933", "2221", "3121", "3361", "4993", "5521", "6481", "8461", "9181", "9901", "10993", "11113", "12241", "12541", "13633", "14173", "17761", "20593", "21433", "21661", "21841", "23773", "26113", "27901", "28393", "29101", "34141", "41161", "49201" ]
[ "nonn" ]
19
1
1
null
[ "M4900", "N2100" ]
N. J. A. Sloane
2023-10-18T10:04:08
oeisdata/seq/A002/A002647.seq
a83af09aa73f9796320c15333c845860
A002648
A variant of the cuban primes: primes p = (x^3 - y^3)/(x - y) where x = y + 2.
[ "13", "109", "193", "433", "769", "1201", "1453", "2029", "3469", "3889", "4801", "10093", "12289", "13873", "18253", "20173", "21169", "22189", "28813", "37633", "43201", "47629", "60493", "63949", "65713", "69313", "73009", "76801", "84673", "106033", "108301", "112909", "115249", "129793", "139969", "142573", "147853", "169933" ]
[ "nonn" ]
61
1
1
[ "A002407", "A002648", "A007645", "A111051" ]
[ "M4910", "N2105" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002648.seq
95b90ec9f0844c7e6fa61ae5808049e2
A002649
Quintan primes: p = (x^5 - y^5)/(x - y).
[ "5", "31", "211", "1031", "2801", "4651", "5261", "6841", "8431", "14251", "17891", "20101", "21121", "22621", "22861", "26321", "30941", "33751", "36061", "41141", "46021", "48871", "51001", "58411", "61051", "88741", "92821", "103801", "109141", "114641", "118061", "125591", "170101", "176641", "209801" ]
[ "nonn" ]
32
1
1
[ "A002649", "A002650" ]
[ "M3964", "N1636" ]
N. J. A. Sloane
2023-10-18T05:00:32
oeisdata/seq/A002/A002649.seq
2b82654774b966e8ca633786600cda53
A002650
Quintan primes: p = (x^5 + y^5)/(x + y).
[ "11", "61", "181", "421", "461", "521", "991", "1621", "1871", "3001", "4441", "4621", "6871", "9091", "9931", "12391", "13421", "14821", "19141", "25951", "35281", "35401", "55201", "58321", "61681", "62071", "72931", "74731", "91331", "92921", "95881", "108421", "117911", "117991", "131041", "132661", "141961" ]
[ "nonn" ]
29
1
1
[ "A002649", "A002650" ]
[ "M4792", "N2044" ]
N. J. A. Sloane
2018-01-11T01:09:03
oeisdata/seq/A002/A002650.seq
b2465071546821d246d799ef52385799
A002651
Dates at 16-day intervals starting at the beginning of a leap year.
[ "16", "1", "17", "4", "20", "5", "21", "7", "23", "8", "24", "10", "26", "11", "27", "12", "28", "14", "30", "15", "1", "17", "2", "18", "3", "19", "7", "23", "8", "24", "10", "26", "11", "27", "13", "29", "14", "30", "15", "1", "17", "2", "18", "4", "20", "5", "21", "6", "22", "10", "26", "11", "27", "13", "29", "14", "30", "16", "1", "17", "2", "18", "4", "20", "5", "21", "7", "23", "8", "24", "9", "25", "13", "29", "14", "30", "16", "1", "17", "3", "19", "4", "20", "5" ]
[ "nonn", "easy" ]
12
1
1
null
null
John Daly (john.daly(AT)cc2smtp.NRCan.gc.ca)
2016-05-14T14:20:57
oeisdata/seq/A002/A002651.seq
c2b54affa720bc4b426f3a74300b2cf0
A002652
Theta series of Kleinian lattice Z[(1 + sqrt(-7))/ 2] in 1 complex (or 2 real) dimensions.
[ "1", "2", "4", "0", "6", "0", "0", "2", "8", "2", "0", "4", "0", "0", "4", "0", "10", "0", "4", "0", "0", "0", "8", "4", "0", "2", "0", "0", "6", "4", "0", "0", "12", "0", "0", "0", "6", "4", "0", "0", "0", "0", "0", "4", "12", "0", "8", "0", "0", "2", "4", "0", "0", "4", "0", "0", "8", "0", "8", "0", "0", "0", "0", "2", "14", "0", "0", "4", "0", "0", "0", "4", "8", "0", "8", "0", "0", "4", "0", "4", "0", "2", "0", "0", "0", "0", "8", "0", "16", "0", "0", "0", "12", "0", "0", "0", "0", "0", "4", "4", "6", "0" ]
[ "nonn", "easy", "nice" ]
64
0
2
[ "A000122", "A000700", "A002652", "A004016", "A004018", "A010054", "A028609", "A028641", "A028951", "A033715", "A035182", "A121373", "A133827", "A138811" ]
null
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002652.seq
3e238b241d7f3879ee1173182f410e44
A002653
Expansion of (theta_3(z)*theta_3(7z)+theta_2(z)*theta_2(7z))^3.
[ "1", "6", "24", "56", "114", "168", "280", "294", "444", "390", "840", "636", "1176", "1176", "1512", "1008", "1782", "2016", "1896", "2520", "3528", "2408", "3216", "2796", "4760", "3174", "5880", "4592", "6258", "4380", "5040", "6720", "7200", "6832", "10080", "7224", "8082", "7164", "12600", "7056", "14280", "11760", "12040", "9756" ]
[ "nonn", "look" ]
30
0
2
[ "A002652", "A002653" ]
null
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002653.seq
4d6b94a1638c325078daa1b98d4096aa
A002654
Number of ways of writing n as a sum of at most two nonzero squares, where order matters; also (number of divisors of n of form 4m+1) - (number of divisors of form 4m+3).
[ "1", "1", "0", "1", "2", "0", "0", "1", "1", "2", "0", "0", "2", "0", "0", "1", "2", "1", "0", "2", "0", "0", "0", "0", "3", "2", "0", "0", "2", "0", "0", "1", "0", "2", "0", "1", "2", "0", "0", "2", "2", "0", "0", "0", "2", "0", "0", "0", "1", "3", "0", "2", "2", "0", "0", "0", "0", "2", "0", "0", "2", "0", "0", "1", "4", "0", "0", "2", "0", "0", "0", "1", "2", "2", "0", "0", "0", "0", "0", "2", "1", "2", "0", "0", "4", "0", "0", "0", "2", "2", "0", "0", "0", "0", "0", "0", "2", "1", "0", "3", "2", "0", "0", "2", "0" ]
[ "core", "easy", "nonn", "nice", "mult" ]
177
1
5
[ "A000089", "A000161", "A000265", "A001481", "A002175", "A002324", "A002325", "A002654", "A003881", "A004018", "A008441", "A014200", "A022544", "A025426", "A027748", "A035170", "A035171", "A035175", "A035179", "A035182", "A035185", "A035187", "A035188", "A035192", "A035194", "A035195", "A035199", "A035203", "A035210", "A035211", "A035215", "A035219", "A101455", "A120630", "A121444", "A122856", "A122865", "A124010", "A143574", "A213408", "A241011" ]
[ "M0012", "N0001" ]
N. J. A. Sloane
2024-12-30T03:31:31
oeisdata/seq/A002/A002654.seq
a75ea6f73aa0fefc0c51d9d6c60201b0
A002655
Expansion of Product_{i >= 1} (1 - q^i)*(1 - q^(7*i)).
[ "1", "-1", "-1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "-2", "0", "-2", "0", "1", "0", "0", "0", "0", "-1", "2", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "-2", "-1", "0", "0", "-1", "0", "2", "0", "0", "0", "0", "0", "0", "2", "-2", "0", "0", "0", "2", "0", "1", "2", "-1", "0", "0", "0", "0", "0", "-2", "-1", "0", "0", "0", "0", "-2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
30
0
13
[ "A002655", "A160806" ]
null
N. J. A. Sloane
2023-10-18T04:36:54
oeisdata/seq/A002/A002655.seq
5ba3bd084cbde179be6cf7062cb80c8c
A002656
Expansion of (eta(q) * eta(q^7))^3 in powers of q.
[ "1", "-3", "0", "5", "0", "0", "-7", "-3", "9", "0", "-6", "0", "0", "21", "0", "-11", "0", "-27", "0", "0", "0", "18", "18", "0", "25", "0", "0", "-35", "-54", "0", "0", "45", "0", "0", "0", "45", "-38", "0", "0", "0", "0", "0", "58", "-30", "0", "-54", "0", "0", "49", "-75", "0", "0", "-6", "0", "0", "21", "0", "162", "0", "0", "0", "0", "-63", "-91", "0", "0", "-118", "0", "0", "0", "114", "-27" ]
[ "sign", "mult" ]
43
1
2
null
null
N. J. A. Sloane
2023-10-18T10:04:13
oeisdata/seq/A002/A002656.seq
e94fa376f4a3b4b7c1a921c0b3a5f7a6
A002657
Numerators of Cauchy numbers of second type (= Bernoulli numbers B_n^{(n)}).
[ "1", "1", "5", "9", "251", "475", "19087", "36799", "1070017", "2082753", "134211265", "262747265", "703604254357", "1382741929621", "8164168737599", "5362709743125", "8092989203533249", "15980174332775873", "12600467236042756559" ]
[ "nonn", "frac", "easy", "nice" ]
139
0
3
[ "A002206", "A002207", "A002208", "A002209", "A002657", "A002790", "A006232", "A006233", "A075266", "A075267", "A262235" ]
[ "M3790", "N1545" ]
N. J. A. Sloane
2025-01-06T10:57:35
oeisdata/seq/A002/A002657.seq
0d39208ce6e382b2518f74c37b490bf9
A002658
a(0) = a(1) = 1; for n > 0, a(n+1) = a(n)*(a(0) + ... + a(n-1)) + a(n)*(a(n) + 1)/2.
[ "1", "1", "2", "7", "56", "2212", "2595782", "3374959180831", "5695183504489239067484387", "16217557574922386301420531277071365103168734284282" ]
[ "nonn", "easy", "core", "nice" ]
106
0
3
[ "A002658", "A005588", "A006894", "A072638" ]
[ "M1814", "N0718" ]
N. J. A. Sloane
2024-12-03T08:24:12
oeisdata/seq/A002/A002658.seq
6396dab7bdbcb5527d952df47b9ffc76
A002659
a(n) = 2*sigma(n) - 1.
[ "1", "5", "7", "13", "11", "23", "15", "29", "25", "35", "23", "55", "27", "47", "47", "61", "35", "77", "39", "83", "63", "71", "47", "119", "61", "83", "79", "111", "59", "143", "63", "125", "95", "107", "95", "181", "75", "119", "111", "179", "83", "191", "87", "167", "155", "143", "95", "247", "113", "185", "143", "195", "107", "239", "143", "239", "159", "179", "119", "335", "123", "191" ]
[ "easy", "nonn" ]
44
1
2
[ "A000203", "A002659", "A002660", "A002791", "A074400", "A242639" ]
[ "M3762", "N1536" ]
N. J. A. Sloane, Simon Plouffe
2017-11-17T04:03:29
oeisdata/seq/A002/A002659.seq
24705834036682a9886cf72b72daa77b
A002660
a(n) = Sum_{d|n, d <= 3} d^2 + 3*Sum_{d|n, d>3} d.
[ "1", "5", "10", "17", "16", "32", "22", "41", "37", "50", "34", "80", "40", "68", "70", "89", "52", "113", "58", "122", "94", "104", "70", "176", "91", "122", "118", "164", "88", "212", "94", "185", "142", "158", "142", "269", "112", "176", "166", "266", "124", "284", "130", "248", "232", "212", "142", "368", "169", "275", "214", "290", "160", "356", "214", "356", "238", "266", "178", "500", "184", "284", "310", "377", "250", "428", "202", "374", "286" ]
[ "nonn" ]
48
1
2
[ "A000203", "A002659", "A002660", "A002791", "A242639" ]
[ "M3797", "N1549" ]
N. J. A. Sloane
2023-03-09T05:04:21
oeisdata/seq/A002/A002660.seq
a54291343b53bbed6a9d3a158a5b0635
A002661
Least integer having Radon random number n.
[ "1", "2", "3", "5", "10", "18", "35", "63", "126", "231", "462", "858", "1716", "3218", "6435", "12155", "24310", "46189", "92378", "176358", "352716", "676039", "1352078", "2600150", "5200300", "10029150", "20058300", "38779380", "77558760", "150270098", "300540195", "583401555", "1166803110", "2268783825", "4537567650" ]
[ "nonn" ]
35
1
2
null
[ "M0723", "N0270" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002661.seq
884081eddfd25501bfdd401f11c62307
A002662
a(n) = 2^n - 1 - n*(n+1)/2.
[ "0", "0", "0", "1", "5", "16", "42", "99", "219", "466", "968", "1981", "4017", "8100", "16278", "32647", "65399", "130918", "261972", "524097", "1048365", "2096920", "4194050", "8388331", "16776915", "33554106", "67108512", "134217349", "268435049", "536870476", "1073741358", "2147483151", "4294966767", "8589934030" ]
[ "easy", "nonn", "nice" ]
188
0
5
[ "A000079", "A000124", "A000217", "A000225", "A000247", "A000290", "A000295", "A001045", "A002662", "A002663", "A002664", "A007318", "A035038", "A035042", "A055248", "A342352" ]
[ "M3866", "N1585" ]
N. J. A. Sloane
2024-08-17T23:02:54
oeisdata/seq/A002/A002662.seq
d88cbff5b98977f9b9cd7b2e64dfce79
A002663
a(n) = 2^n - C(n,0) - C(n,1) - C(n,2) - C(n,3).
[ "0", "0", "0", "0", "1", "6", "22", "64", "163", "382", "848", "1816", "3797", "7814", "15914", "32192", "64839", "130238", "261156", "523128", "1047225", "2095590", "4192510", "8386560", "16774891", "33551806", "67105912", "134214424", "268431773", "536866822", "1073737298" ]
[ "nonn", "easy" ]
69
0
6
[ "A000079", "A000225", "A000295", "A002662", "A002663", "A002664", "A007318", "A035038", "A035042", "A055248" ]
[ "M4152", "N1725" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002663.seq
c6e4017a6de61792181c3a3b82090d0b
A002664
a(n) = 2^n - C(n,0)- ... - C(n,4).
[ "0", "0", "0", "0", "0", "1", "7", "29", "93", "256", "638", "1486", "3302", "7099", "14913", "30827", "63019", "127858", "258096", "519252", "1042380", "2089605", "4185195", "8377705", "16764265", "33539156", "67090962", "134196874", "268411298", "536843071", "1073709893" ]
[ "nonn", "easy" ]
73
0
7
[ "A000079", "A000225", "A000295", "A002662", "A002663", "A002664", "A007318", "A035038", "A035042", "A055248" ]
[ "M4395", "N1851" ]
N. J. A. Sloane
2025-03-09T12:28:39
oeisdata/seq/A002/A002664.seq
3658546a8024e58d500aeae68e743666
A002665
Continued fraction expansion of Lehmer's constant.
[ "0", "1", "1", "2", "5", "34", "985", "1151138", "1116929202845", "1480063770341062927127746", "1846425204836010506550936273411258268076151412465" ]
[ "nonn", "cofr", "nice", "easy" ]
37
0
4
[ "A002065", "A002665", "A002794", "A002795", "A030125", "A096407" ]
[ "M1549", "N0605" ]
N. J. A. Sloane
2016-01-21T09:00:45
oeisdata/seq/A002/A002665.seq
259bb570d674c9770234cf914f591447
A002666
Continued cotangent for square root of 2.
[ "1", "5", "36", "3406", "14694817", "727050997716715", "2074744506784679417243551677046", "46045625970633183674340934067371917846908361831894602280765110" ]
[ "nonn", "changed" ]
36
0
2
null
[ "M3983", "N1652" ]
N. J. A. Sloane
2025-04-25T03:15:53
oeisdata/seq/A002/A002666.seq
c21bdfbe0a8e2e807a5e409cd8ddf3b3
A002667
Continued cotangent for Pi.
[ "3", "73", "8599", "400091364", "371853741549033970", "253461181173408820488703379557217678" ]
[ "nonn", "changed" ]
27
0
1
null
[ "M3171", "N1286" ]
N. J. A. Sloane
2025-04-24T17:35:12
oeisdata/seq/A002/A002667.seq
2c47e21b4f57f1ea775b779cb834d573
A002668
Continued cotangent for e.
[ "2", "8", "75", "8949", "119646723", "15849841722437093", "708657580163382065836292133774995", "529026553215766321676623343348414600292754204772300344704877695232" ]
[ "nonn", "easy", "nice" ]
32
1
1
null
[ "M1900", "N0748" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002668.seq
d0006c30a149598bedec0b8169088bd7
A002669
Numerator of constant term in polynomial arising from numerical integration formula.
[ "-1", "3", "-29", "289", "-1627", "27769", "-18044381", "145511171", "-1514611753", "142324922009", "-45517196560877", "1750347891902329", "-307338038704738637", "32691361126849302587", "-124979231585030156687", "13342245096512975609370931", "-265966517264946845952131041" ]
[ "sign", "frac" ]
20
1
2
[ "A002669", "A002670" ]
[ "M3119", "N1264" ]
N. J. A. Sloane
2023-10-18T04:32:52
oeisdata/seq/A002/A002669.seq
3017aa2a213bcd18e8cff41c33438439
A002670
Denominator of constant term in polynomial arising from numerical integration formula.
[ "1", "2", "12", "72", "240", "2400", "907200", "4233600", "25401600", "1371686400", "251475840000", "5532468480000", "554827553280000", "33659538232320000", "73302994372608000", "4453156908135936000000", "50469111625540608000000", "63553696121051136000000" ]
[ "nonn" ]
19
1
2
[ "A002669", "A002670" ]
[ "M2033", "N0805" ]
N. J. A. Sloane
2023-10-19T08:18:40
oeisdata/seq/A002/A002670.seq
188ad6ecb541baf512f15c36d26bc28d
A002671
a(n) = 4^n*(2*n+1)!.
[ "1", "24", "1920", "322560", "92897280", "40874803200", "25505877196800", "21424936845312000", "23310331287699456000", "31888533201572855808000", "53572735778642397757440000", "108431217215972213061058560000" ]
[ "nonn", "easy" ]
72
0
2
[ "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677", "A002866", "A007346", "A225076" ]
[ "M5174", "N2246" ]
N. J. A. Sloane and Simon Plouffe
2025-02-16T08:32:26
oeisdata/seq/A002/A002671.seq
f1d440cdd35a0222c7b1ac16738efca5
A002672
Denominators of central difference coefficients M_{3}^(2n+1).
[ "1", "8", "1920", "193536", "154828800", "1167851520", "892705701888000", "1428329123020800", "768472460034048000", "4058540589291090739200", "196433364521688791777280000", "5957759187690780937420800000", "30447485794244997427545243648000000", "341011840895543971188506728857600000" ]
[ "nonn", "frac" ]
31
1
2
[ "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677" ]
[ "M4588", "N1957" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002672.seq
bd86ea69308c299ded09a0bdaedc534c
A002673
Numerators of central difference coefficients M_{3}^(2n+1).
[ "1", "1", "13", "41", "671", "73", "597871", "7913", "28009", "792451", "170549237", "19397633", "317733228541", "9860686403", "75397891", "170314355593", "2084647712458321", "29327731093", "168856464709124011", "3063310184201", "499338236699611", "535201577273701757", "23571643935246013553" ]
[ "nonn", "frac" ]
33
1
3
[ "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677" ]
[ "M4894", "N2097" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002673.seq
fc16f054e64cd732227901ae00c614dc
A002674
a(n) = (2n)!/2.
[ "1", "12", "360", "20160", "1814400", "239500800", "43589145600", "10461394944000", "3201186852864000", "1216451004088320000", "562000363888803840000", "310224200866619719680000", "201645730563302817792000000", "152444172305856930250752000000", "132626429906095529318154240000000" ]
[ "nonn", "easy" ]
64
1
2
[ "A000142", "A002544", "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677", "A010050", "A090438" ]
[ "M4879", "N2092" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:26
oeisdata/seq/A002/A002674.seq
651a9f36c8c97d41c2f4a34aec530d73
A002675
Numerators of coefficients for central differences M_{4}^(2*n).
[ "1", "1", "1", "17", "31", "1", "5461", "257", "73", "1271", "60787", "241", "22369621", "617093", "49981", "16843009", "5726623061", "7957", "91625968981", "61681", "231927781", "50991843607", "499069107643", "4043309297", "1100586419201", "5664905191661", "1672180312771" ]
[ "nonn", "frac" ]
35
2
4
[ "A002430", "A002431", "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677" ]
[ "M5035", "N2173" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002675.seq
c120fad17034e5a0872210c63dd6d4bf
A002676
Denominators of coefficients for central differences M_{4}^(2*n).
[ "1", "6", "80", "30240", "1814400", "2661120", "871782912000", "3138418483200", "84687482880000", "170303140572364800", "1124000727777607680000", "724146127139635200000", "12703681025488077520896000000", "76222086152928465125376000000", "1531041037877004667453440000000" ]
[ "nonn", "frac" ]
32
2
2
[ "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677" ]
[ "M4282", "N1789" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002676.seq
71ac049bbc38a9379dfa92fc025b9803
A002677
Denominators of coefficients for central differences M_{3}'^(2*n+1).
[ "1", "4", "40", "12096", "604800", "760320", "217945728000", "697426329600", "16937496576000", "30964207376793600", "187333454629601280000", "111407096483020800000", "1814811575069725360128000000", "10162944820390462016716800000" ]
[ "nonn", "frac" ]
38
1
2
[ "A002671", "A002672", "A002673", "A002674", "A002675", "A002676", "A002677" ]
[ "M3676", "N1499" ]
N. J. A. Sloane
2019-10-09T07:21:25
oeisdata/seq/A002/A002677.seq
92133835b446c552bdd5ce7677c54c2e
A002678
Numerators of the Taylor coefficients of (e^x-1)^2.
[ "1", "1", "7", "1", "31", "1", "127", "17", "73", "31", "2047", "1", "8191", "5461", "4681", "257", "131071", "73", "524287", "1271", "42799", "60787", "8388607", "241", "33554431", "22369621", "19173961", "617093", "536870911", "49981", "2147483647", "16843009", "53353631", "5726623061", "1108378657" ]
[ "nonn", "frac" ]
38
2
3
[ "A000142", "A002678", "A002679", "A065974", "A065975", "A324003", "A324004", "A324005", "A324006" ]
[ "M4321", "N1810" ]
N. J. A. Sloane
2019-02-15T13:55:29
oeisdata/seq/A002/A002678.seq
6880d43accd98f62ce7b6a438c60bbd4
A002679
Denominator of 2*Stirling_2(n,2)/n!.
[ "1", "1", "12", "4", "360", "40", "20160", "12096", "259200", "604800", "239500800", "760320", "43589145600", "217945728000", "1494484992000", "697426329600", "3201186852864000", "16937496576000", "1216451004088320000", "30964207376793600", "11469395181404160000" ]
[ "nonn", "frac" ]
25
2
3
[ "A002678", "A002679" ]
[ "M4820", "N2062" ]
N. J. A. Sloane
2019-02-15T13:52:15
oeisdata/seq/A002/A002679.seq
5d8d3df38ced19329ba4bbcf893fda75
A002680
Denominators of coefficients of polynomials arising from Chebyshev quadrature.
[ "1", "1", "3", "2", "45", "72", "105", "6480", "42525", "22400", "56133", "32659200", "7882875", "452656512000", "351833625", "129153024", "4396161144375", "8473729904640000", "9901766875", "54452188367216640000", "4167666272734965", "168568418304000000", "7426884628582453125", "20484913263746899968000000" ]
[ "nonn", "easy", "frac" ]
64
0
3
[ "A002680", "A101270", "A324123" ]
[ "M2261", "N0892" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002680.seq
abf2568d4bf25e17e8aeb3a5addb6e79
A002681
Numerators of coefficients for repeated integration.
[ "1", "-1", "1", "-23", "263", "-133787", "157009", "-16215071", "2689453969", "-26893118531", "5600751928169", "-3340626516019229", "885646796787371", "-859202038021848149", "2766671664340938282413", "-319473088311274492668499", "436677987276721765221113", "-191960665849028069896950959123" ]
[ "sign", "frac" ]
20
0
4
[ "A002195", "A002196", "A002681", "A002682" ]
[ "M5136", "N2227" ]
N. J. A. Sloane
2021-10-04T12:36:06
oeisdata/seq/A002/A002681.seq
707cc71829bd90775645c9d608bed23c
A002682
Denominators of coefficients for repeated integration.
[ "3", "45", "252", "28350", "1496880", "3405402000", "17513496000", "7815397590000", "5543722023840000", "235212205868640000", "206559082608278400000", "516914104227216696000000", "572581776990147724800000" ]
[ "nonn", "frac" ]
22
0
1
[ "A002195", "A002196", "A002681", "A002682" ]
[ "M3152", "N1277" ]
N. J. A. Sloane
2021-10-04T12:37:10
oeisdata/seq/A002/A002682.seq
b1a90b1c999db2d7b6f1a2abba72c0cd
A002683
Numerators of coefficients for repeated integration.
[ "1", "-7", "37", "-199", "40321", "-5512813", "136601407", "-32373535937", "4039314145093", "-377880467185583", "123905113265594071", "-53834048464836263969", "66351862106782030159", "-194322297839115779164331", "149128127842572749235559291", "-25454412383565669030714950177" ]
[ "sign", "frac" ]
19
0
2
[ "A002195", "A002196", "A002683", "A002684" ]
[ "M4421", "N1868" ]
N. J. A. Sloane
2021-12-20T20:56:57
oeisdata/seq/A002/A002683.seq
0d86a04fcfff7b3f7f90dc852550b029
A002684
Denominators of coefficients for repeated integration.
[ "6", "360", "10080", "259200", "239500800", "145297152000", "15692092416000", "16005934264320000", "8515157028618240000", "3372002183332823040000", "4653363012999295795200000", "8469120683658718347264000000" ]
[ "nonn", "frac" ]
18
0
1
[ "A002195", "A002196", "A002683", "A002684" ]
[ "M4307", "N1802" ]
N. J. A. Sloane
2021-12-20T20:20:32
oeisdata/seq/A002/A002684.seq
8c622e0acb56fcb0fa1d0059fa2713fd
A002685
Coefficients for numerical integration.
[ "2", "6", "34", "250", "972", "15498", "766808", "5961306", "54891535", "2488870076" ]
[ "nonn" ]
34
1
1
[ "A002685", "A002686", "A324124", "A328866", "A328884", "A328885" ]
[ "M1702", "N0671" ]
N. J. A. Sloane
2019-10-30T03:43:14
oeisdata/seq/A002/A002685.seq
37962cfa7fc321b66d38ace968133285
A002686
Coefficients for numerical integration.
[ "1", "8", "45", "416", "1685", "31032", "1603182", "13856896", "132843888", "6551143600" ]
[ "nonn" ]
29
1
2
[ "A002685", "A002686", "A324124", "A328866", "A328884", "A328885" ]
[ "M4533", "N1922" ]
N. J. A. Sloane
2019-10-30T03:42:48
oeisdata/seq/A002/A002686.seq
e58637bab595f067b13fdf955e6fcf0f
A002687
Numerators of coefficients for repeated integration.
[ "1", "-1", "1", "-7", "107", "-199", "6031", "-5741", "1129981", "-435569", "35661419", "-1523489833", "45183033541", "-12597680311", "19055094997949", "-9331210633373", "104148936040729", "-2250170748719203", "734854328394419537", "-826511503463860961" ]
[ "sign", "frac" ]
33
1
4
[ "A002687", "A002688" ]
[ "M4457", "N1887" ]
N. J. A. Sloane
2023-10-19T08:48:00
oeisdata/seq/A002/A002687.seq
9f7b7cba42208aebba1c85567a4f5918
A002688
Denominators of coefficients for repeated integration.
[ "6", "24", "45", "480", "10080", "24192", "907200", "1036800", "239500800", "106444800", "9906624000", "475517952000", "15692092416000", "4828336128000", "8002967132160000", "4268249137152000", "51607012294656000", "1202139815804928000" ]
[ "nonn", "frac" ]
33
1
1
[ "A002687", "A002688" ]
[ "M4158", "N1728" ]
N. J. A. Sloane
2023-10-19T12:51:46
oeisdata/seq/A002/A002688.seq
f5fe4226660a88c5bbee18de1b7aefff
A002689
Denominators of coefficients for repeated integration.
[ "2", "6", "8", "180", "32", "10080", "3456", "453600", "115200", "47900160", "71680", "217945728000", "36578304000", "2241727488000", "45984153600", "2000741783040000", "918421504", "43667471941632000", "5751865147392000", "240857298809487360000" ]
[ "nonn", "frac" ]
26
0
1
null
[ "M4072", "N1687" ]
N. J. A. Sloane
2023-10-19T08:24:43
oeisdata/seq/A002/A002689.seq
2e6d3c932c44d548567f7e11465376f7
A002690
a(n) = (n+1) * (2*n)! / n!.
[ "1", "4", "36", "480", "8400", "181440", "4656960", "138378240", "4670265600", "176432256000", "7374868300800", "337903056691200", "16838835658444800", "906706535454720000", "52459449551308800000", "3245491278907637760000", "213796737998040637440000", "14940619102451310428160000", "1103945744792235714969600000" ]
[ "nonn", "easy", "nice" ]
43
0
2
[ "A000407", "A001193", "A001813", "A002690", "A002691", "A245334" ]
[ "M3665", "N1491" ]
N. J. A. Sloane
2025-01-22T11:31:50
oeisdata/seq/A002/A002690.seq
b87689ce53caa0b6606f801f2b873e6a
A002691
a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.
[ "1", "9", "120", "2100", "45360", "1164240", "34594560", "1167566400", "44108064000", "1843717075200", "84475764172800", "4209708914611200", "226676633863680000", "13114862387827200000", "811372819726909440000", "53449184499510159360000", "3735154775612827607040000" ]
[ "nonn", "easy", "nice" ]
37
0
2
[ "A002690", "A002691" ]
[ "M4661", "N1996" ]
N. J. A. Sloane
2017-10-13T15:46:22
oeisdata/seq/A002/A002691.seq
1c10b9e1d85dd0de57850fe44002e9cc
A002692
Not integral, withdrawn.
[ "1", "2", "5", "17", "55", "186", "635", "2199", "7691", "27101", "96061" ]
[ "dead" ]
11
0
2
null
[ "M1508", "N0593" ]
null
2015-07-25T10:47:02
oeisdata/seq/A002/A002692.seq
f72ed1306d4da84b06ae6ecb2baaf8a6
A002693
Not integral, withdrawn.
[ "0", "1", "6", "28", "125", "527", "2168", "8781", "35155", "139531", "550068" ]
[ "dead" ]
10
0
3
null
[ "M4184", "N1742" ]
null
2015-07-25T10:49:07
oeisdata/seq/A002/A002693.seq
d7cd93f4d0ff4720d8ac6757e3b1ff17
A002694
Binomial coefficients C(2n, n-2).
[ "1", "6", "28", "120", "495", "2002", "8008", "31824", "125970", "497420", "1961256", "7726160", "30421755", "119759850", "471435600", "1855967520", "7307872110", "28781143380", "113380261800", "446775310800", "1761039350070", "6943526580276", "27385657281648", "108043253365600" ]
[ "nonn", "easy", "changed" ]
160
2
2
[ "A000027", "A000984", "A001622", "A001700", "A001791", "A002054", "A002694", "A002696", "A003516", "A004310", "A004318", "A004321", "A004334", "A004347", "A004361", "A004375", "A004389", "A006659", "A009766", "A030053", "A030056", "A100257", "A281580" ]
[ "M4181", "N1741" ]
N. J. A. Sloane
2025-04-26T10:25:00
oeisdata/seq/A002/A002694.seq
ea5c750150bfe681ec79e659fe94acd9
A002695
P_n'(3), where P_n is n-th Legendre polynomial.
[ "1", "9", "66", "450", "2955", "18963", "119812", "748548", "4637205", "28537245", "174683718", "1064611782", "6464582943", "39132819495", "236256182280", "1423046656008", "8554078990377", "51327262010673", "307488810131530", "1839455028693450" ]
[ "nonn", "easy" ]
46
1
2
[ "A001850", "A002695" ]
[ "M4642", "N1985" ]
N. J. A. Sloane, Simon Plouffe
2024-09-28T07:36:30
oeisdata/seq/A002/A002695.seq
0c8972831d216776dc8d65cf5d5ab105
A002696
Binomial coefficients C(2n,n-3).
[ "1", "8", "45", "220", "1001", "4368", "18564", "77520", "319770", "1307504", "5311735", "21474180", "86493225", "347373600", "1391975640", "5567902560", "22239974430", "88732378800", "353697121050", "1408831480056", "5608233007146", "22314239266528", "88749815264600", "352870329957600", "1402659561581460" ]
[ "nonn", "easy" ]
85
3
2
[ "A000984", "A001622", "A001700", "A001791", "A002054", "A002694", "A002696", "A003516", "A004310", "A004318", "A030053", "A030056", "A100257", "A263776" ]
[ "M4532", "N1921" ]
N. J. A. Sloane
2024-10-14T10:56:36
oeisdata/seq/A002/A002696.seq
e054399ad4a971376ce8da7b8f8f788f
A002697
a(n) = n*4^(n-1).
[ "0", "1", "8", "48", "256", "1280", "6144", "28672", "131072", "589824", "2621440", "11534336", "50331648", "218103808", "939524096", "4026531840", "17179869184", "73014444032", "309237645312", "1305670057984", "5497558138880", "23089744183296" ]
[ "nonn", "easy" ]
226
0
3
[ "A000051", "A000302", "A000984", "A001792", "A002457", "A002697", "A002699", "A027656", "A038231", "A082134", "A083672", "A125145", "A128235", "A133224", "A212698" ]
[ "M4534", "N1923" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002697.seq
3130e84d206d4d360e9d13dc85cb6678
A002698
Coefficients of Chebyshev polynomials: n*(2*n-3)*2^(2*n-5).
[ "1", "18", "160", "1120", "6912", "39424", "212992", "1105920", "5570560", "27394048", "132120576", "627048448", "2936012800", "13589544960", "62277025792", "282930970624", "1275605286912", "5712306503680", "25426206392320", "112562502893568", "495879744126976", "2174833999740928", "9499780463984640" ]
[ "nonn" ]
42
2
2
[ "A000079", "A002698", "A014107" ]
[ "M5059", "N2189" ]
N. J. A. Sloane
2023-10-19T08:25:44
oeisdata/seq/A002/A002698.seq
70a103de348e6e968e69e4ea6e607040
A002699
a(n) = n*2^(2*n-1).
[ "0", "2", "16", "96", "512", "2560", "12288", "57344", "262144", "1179648", "5242880", "23068672", "100663296", "436207616", "1879048192", "8053063680", "34359738368", "146028888064", "618475290624", "2611340115968", "10995116277760", "46179488366592", "193514046488576" ]
[ "nonn", "easy", "nice" ]
85
0
2
[ "A000051", "A002457", "A002697", "A002699", "A053124", "A053125", "A212698" ]
[ "M2090", "N0825" ]
N. J. A. Sloane
2023-07-11T12:19:28
oeisdata/seq/A002/A002699.seq
84687a1e927eb18dcb3bea4a096d7065
A002700
Coefficients of Chebyshev polynomials: n*(2*n+1) * 4^(n-1).
[ "3", "40", "336", "2304", "14080", "79872", "430080", "2228224", "11206656", "55050240", "265289728", "1258291200", "5888802816", "27246198784", "124822487040", "566935683072", "2555505541120", "11441792876544", "50921132261376", "225399883694080", "992858999881728", "4354066045992960" ]
[ "nonn", "easy" ]
50
1
1
[ "A002699", "A002700" ]
[ "M3147", "N1275" ]
N. J. A. Sloane
2023-02-17T08:15:47
oeisdata/seq/A002/A002700.seq
bacb5a5cbeba65aa59c26d3c428e6cab