Datasets:
christopher
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oeis

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1999-12-11 03:00:00
2025-04-25 01:21:50
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A002801
a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) with a(0) = a(1) = 1.
[ "1", "1", "2", "8", "50", "418", "4348", "54016", "779804", "12824540", "236648024", "4841363104", "108748223128", "2660609220952", "70422722065040", "2005010410792832", "61098981903602192", "1984186236246187024", "68407835576255308576", "2495374564069015050880", "96019859122742736121376", "3886906732751071879958816", "165120572466718493379680192" ]
[ "nonn" ]
50
0
5
[ "A002801", "A247249" ]
[ "M1882", "N0744" ]
N. J. A. Sloane
2015-10-30T11:42:38
oeisdata/seq/A002/A002801.seq
dca8a1fa2e22d234e5258eaee5a21dc7
A002802
a(n) = (2*n+3)!/(6*n!*(n+1)!).
[ "1", "10", "70", "420", "2310", "12012", "60060", "291720", "1385670", "6466460", "29745716", "135207800", "608435100", "2714556600", "12021607800", "52895074320", "231415950150", "1007340018300", "4365140079300", "18839025605400", "81007810103220", "347176329013800", "1483389769422600" ]
[ "nonn", "easy" ]
147
0
5
[ "A000108", "A000911", "A000984", "A002457", "A002697", "A002802", "A035309", "A046521", "A051133", "A370235" ]
[ "M4724", "N2019" ]
N. J. A. Sloane
2024-12-27T22:37:32
oeisdata/seq/A002/A002802.seq
c4676dacae5fcccc1e6114124e11bfb9
A002803
a(n) = (2n+4)!/(4!*n!*(n+1)!).
[ "1", "15", "140", "1050", "6930", "42042", "240240", "1312740", "6928350", "35565530", "178474296", "878850700", "4259045700", "20359174500", "96172862400", "449608131720", "2082743551350", "9569730173850", "43651400793000", "197809768856700" ]
[ "nonn", "easy" ]
30
0
5
[ "A002803", "A020918" ]
[ "M4980", "N2140" ]
N. J. A. Sloane
2021-05-09T06:08:09
oeisdata/seq/A002/A002803.seq
0587807aab7d30b92c180d8fbd3c724c
A002804
(Presumed) solution to Waring's problem: g(n) = 2^n + floor((3/2)^n) - 2.
[ "1", "4", "9", "19", "37", "73", "143", "279", "548", "1079", "2132", "4223", "8384", "16673", "33203", "66190", "132055", "263619", "526502", "1051899", "2102137", "4201783", "8399828", "16794048", "33579681", "67146738", "134274541", "268520676", "536998744", "1073933573", "2147771272", "4295398733", "8590581749" ]
[ "nonn", "easy", "changed" ]
101
0
5
[ "A002376", "A002377", "A002804", "A079611", "A174406", "A174420", "A297446" ]
[ "M3361", "N1353" ]
N. J. A. Sloane
2025-04-20T01:13:40
oeisdata/seq/A002/A002804.seq
b83f0f41781aa30ba5bd3f892646c6a8
A002805
Denominators of harmonic numbers H(n) = Sum_{i=1..n} 1/i.
[ "1", "2", "6", "12", "60", "20", "140", "280", "2520", "2520", "27720", "27720", "360360", "360360", "360360", "720720", "12252240", "4084080", "77597520", "15519504", "5173168", "5173168", "118982864", "356948592", "8923714800", "8923714800", "80313433200", "80313433200", "2329089562800", "2329089562800", "72201776446800" ]
[ "nonn", "easy", "frac", "nice" ]
174
0
5
[ "A001008", "A002110", "A002805", "A007406", "A007407", "A007408", "A007409", "A024451", "A025529", "A027611", "A027612", "A034386", "A075135", "A106830", "A203810", "A203811", "A203812", "A250133", "A282511", "A282512", "A296358" ]
[ "M1589", "N0619" ]
N. J. A. Sloane
2025-03-22T13:33:36
oeisdata/seq/A002/A002805.seq
50a4624bba0b832ae8fff771a71bfc6f
A002806
Number of ways of getting nothing, a pair, 2 pair, 3 of a kind, other straight, other flush, full house, 4 of a kind, other straight flush, or a royal flush in 5-card poker.
[ "1302540", "1098240", "123552", "54912", "10200", "5108", "3744", "624", "36", "4" ]
[ "fini", "full", "nonn" ]
14
0
5
[ "A002761", "A002806" ]
null
N. J. A. Sloane, Koreen M Mielke (mielkk72(AT)VAXA.CIS.UWOSH.EDU)
2019-04-09T05:12:56
oeisdata/seq/A002/A002806.seq
95da6f720ba3e01114c2231a0cc881d5
A002807
a(n) = Sum_{k=3..n} (k-1)!*C(n,k)/2.
[ "0", "0", "0", "1", "7", "37", "197", "1172", "8018", "62814", "556014", "5488059", "59740609", "710771275", "9174170011", "127661752406", "1904975488436", "30341995265036", "513771331467372", "9215499383109573", "174548332364311563", "3481204991988351553", "72920994844093191553", "1600596371590399671784" ]
[ "nonn", "easy", "nice" ]
66
0
5
[ "A002807", "A070968", "A099198", "A099201", "A117130", "A284947" ]
[ "M4420", "N1867" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002807.seq
64e11bc516f380eca288812d981e5779
A002808
The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
[ "4", "6", "8", "9", "10", "12", "14", "15", "16", "18", "20", "21", "22", "24", "25", "26", "27", "28", "30", "32", "33", "34", "35", "36", "38", "39", "40", "42", "44", "45", "46", "48", "49", "50", "51", "52", "54", "55", "56", "57", "58", "60", "62", "63", "64", "65", "66", "68", "69", "70", "72", "74", "75", "76", "77", "78", "80", "81", "82", "84", "85", "86", "87", "88" ]
[ "nonn", "nice", "easy", "core" ]
322
0
5
[ "A000040", "A000720", "A002808", "A008578", "A018252", "A035250", "A060715", "A063124", "A065090", "A065855", "A070046", "A073445", "A073783", "A075084", "A077463", "A108954", "A136527", "A163870", "A230954", "A230955", "A246514", "A307912", "A307989", "A376759", "A376760", "A376761" ]
[ "M3272", "N1322" ]
N. J. A. Sloane
2025-04-04T22:34:52
oeisdata/seq/A002/A002808.seq
d344b5f0ae51a69befcdc8c3cdd3d78b
A002809
Increasing values of A000793 (largest order of permutation of n elements).
[ "1", "2", "3", "4", "6", "12", "15", "20", "30", "60", "84", "105", "140", "210", "420", "840", "1260", "1540", "2310", "2520", "4620", "5460", "9240", "13860", "16380", "27720", "30030", "32760", "60060", "120120", "180180", "360360", "471240", "510510", "556920", "1021020", "1141140", "2042040", "3063060", "3423420", "6126120", "6846840" ]
[ "nonn", "nice" ]
47
0
5
[ "A000793", "A002809", "A006644" ]
[ "M0577", "N0210" ]
N. J. A. Sloane
2023-10-29T13:07:23
oeisdata/seq/A002/A002809.seq
8796e1094c9e5b4679b9d0288bf74da0
A002810
Smallest number containing n syllables in UK English.
[ "1", "7", "11", "27", "77", "107", "111", "127", "177", "777", "1127", "1177", "1777", "7777", "11777", "27777", "77777", "107777", "111777", "127777", "177777", "777777", "1127777", "1177777", "1777777", "7777777", "11777777", "27777777", "77777777", "107777777", "111777777", "127777777", "177777777", "777777777" ]
[ "word", "nonn" ]
68
0
5
[ "A002810", "A045736" ]
[ "M4341", "N1818" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002810.seq
69949c77a2bd2a3f1d2a58236958c605
A002811
Erroneous version of A002439.
[ "1", "5", "23", "1681", "257543", "67637281", "27138236663", "15442193173681" ]
[ "dead" ]
15
0
5
null
[ "M3927", "N1615" ]
null
2017-06-01T23:26:51
oeisdata/seq/A002/A002811.seq
059db95450e5aca351b11a097687fb7e
A002812
a(n) = 2*a(n-1)^2 - 1, starting a(0) = 2.
[ "2", "7", "97", "18817", "708158977", "1002978273411373057", "2011930833870518011412817828051050497", "8095731360557835890888779535060256832479295062749579257164654370487894017" ]
[ "nonn", "easy", "nice" ]
101
0
5
[ "A001075", "A002531", "A002812", "A003010", "A071579", "A177879" ]
[ "M1817", "N0720" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002812.seq
49b2153408b3b53c90abc140aed6633c
A002813
a(0) = 4; for n > 0, a(n) = a(n-1)^3 - 3*a(n-1)^2 + 3.
[ "4", "19", "5779", "192900153619", "7177905237579946589743592924684179", "369822356418414944143680173221426891716916679027557977938929258031490127514207143830378340325399155219" ]
[ "nonn", "easy", "nice" ]
58
0
5
[ "A002813", "A002814", "A006267" ]
[ "M3561", "N1443" ]
N. J. A. Sloane
2025-01-08T09:26:05
oeisdata/seq/A002/A002813.seq
77792183ca41e83a0d4b8a7be42f4506
A002814
For n > 1: a(n) = a(n-1)^3 + 3a(n-1)^2 - 3; a(0) = 1, a(1) = 2.
[ "1", "2", "17", "5777", "192900153617", "7177905237579946589743592924684177" ]
[ "nonn", "easy", "nice" ]
78
0
5
[ "A000045", "A000244", "A001566", "A001999", "A002814", "A045529", "A145502", "A219162" ]
[ "M2105", "N0833" ]
N. J. A. Sloane
2022-12-08T12:39:14
oeisdata/seq/A002/A002814.seq
f894aae94314e7dd21089aab966bcabd
A002815
a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.
[ "0", "1", "3", "6", "9", "13", "17", "22", "27", "32", "37", "43", "49", "56", "63", "70", "77", "85", "93", "102", "111", "120", "129", "139", "149", "159", "169", "179", "189", "200", "211", "223", "235", "247", "259", "271", "283", "296", "309", "322", "335", "349", "363", "378", "393", "408", "423", "439", "455", "471" ]
[ "nonn", "nice", "easy" ]
63
0
5
[ "A000720", "A002815", "A046992" ]
[ "M2523", "N0996" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2024-02-17T08:17:32
oeisdata/seq/A002/A002815.seq
b5ebe2363d70ddc833a4d8a5bff286ee
A002816
Number of polygons that can be formed from n points on a circle, no two adjacent.
[ "1", "0", "0", "0", "1", "3", "23", "177", "1553", "14963", "157931", "1814453", "22566237", "302267423", "4340478951", "66541218865", "1084982173641", "18752743351339", "342523093859011", "6593167693927885", "133408305489947029", "2831112931136162775", "62878579846490149375", "1458746608689369440265" ]
[ "nonn", "nice", "easy" ]
58
0
5
[ "A000179", "A002816", "A006184", "A078603", "A078630", "A078631", "A242522", "A326411" ]
[ "M3102", "N1257" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002816.seq
1f695652fb2b8268dacc291164315824
A002817
Doubly triangular numbers: a(n) = n*(n+1)*(n^2+n+2)/8.
[ "0", "1", "6", "21", "55", "120", "231", "406", "666", "1035", "1540", "2211", "3081", "4186", "5565", "7260", "9316", "11781", "14706", "18145", "22155", "26796", "32131", "38226", "45150", "52975", "61776", "71631", "82621", "94830", "108345", "123256", "139656", "157641", "177310", "198765", "222111", "247456", "274911", "304590" ]
[ "nonn", "easy", "nice" ]
222
0
5
[ "A000217", "A000292", "A000332", "A001496", "A001621", "A002721", "A002817", "A005045", "A006003", "A006528", "A007204", "A016754", "A060446", "A064322", "A066370", "A165211", "A178238", "A236770", "A257493", "A302695", "A331436", "A343097" ]
[ "M4141", "N1718" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002817.seq
aafa561ca9b1bade1c40e75f8bead25f
A002818
Nearest integer to exp n^2.
[ "1", "3", "55", "8103", "8886111", "72004899337", "4311231547115195", "1907346572495099690525", "6235149080811616882909238709", "150609731458503054835259413016767498", "26881171418161354484126255515800135873611119", "35451311827611664751894074212478186938177865767023505" ]
[ "nonn" ]
14
0
5
null
[ "M3162", "N1280" ]
N. J. A. Sloane
2023-09-29T22:10:21
oeisdata/seq/A002/A002818.seq
9eadcf8031e3b92b0462afb6255285b2
A002819
Liouville's function L(n) = partial sums of A008836.
[ "0", "1", "0", "-1", "0", "-1", "0", "-1", "-2", "-1", "0", "-1", "-2", "-3", "-2", "-1", "0", "-1", "-2", "-3", "-4", "-3", "-2", "-3", "-2", "-1", "0", "-1", "-2", "-3", "-4", "-5", "-6", "-5", "-4", "-3", "-2", "-3", "-2", "-1", "0", "-1", "-2", "-3", "-4", "-5", "-4", "-5", "-6", "-5", "-6", "-5", "-6", "-7", "-6", "-5", "-4", "-3", "-2", "-3", "-2", "-3", "-2", "-3", "-2", "-1", "-2", "-3", "-4", "-3", "-4", "-5", "-6", "-7", "-6", "-7", "-8", "-7", "-8", "-9", "-10", "-9", "-8", "-9", "-8", "-7", "-6" ]
[ "nice", "sign" ]
86
0
5
[ "A002053", "A002819", "A008836", "A028488", "A239122", "A360659" ]
[ "M0042", "N0012" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002819.seq
679ec48c31bdcb13ed44ab6aee31cc0b
A002820
Number of n X n invertible binary matrices A such that A+I is invertible.
[ "1", "0", "2", "48", "5824", "2887680", "5821595648", "47317927329792", "1544457148312846336", "202039706313624586813440", "105823549214125066767168438272", "221819704567105547916502447159246848", "1860304261534304703934696550224148083769344", "62413833036707798343389591015829588620560344023040" ]
[ "nonn", "nice", "easy" ]
56
0
5
[ "A002820", "A002884", "A346201", "A346381" ]
[ "M2170", "N0866" ]
N. J. A. Sloane
2025-01-10T18:14:52
oeisdata/seq/A002/A002820.seq
4b909de3a72833bc4d172dd9a9d47ab3
A002821
a(n) = nearest integer to n^(3/2).
[ "0", "1", "3", "5", "8", "11", "15", "19", "23", "27", "32", "36", "42", "47", "52", "58", "64", "70", "76", "83", "89", "96", "103", "110", "118", "125", "133", "140", "148", "156", "164", "173", "181", "190", "198", "207", "216", "225", "234", "244", "253", "263", "272", "282", "292", "302", "312", "322", "333", "343", "354", "364", "375", "386", "397" ]
[ "nonn", "easy", "nice" ]
33
0
5
[ "A000093", "A002821", "A077118" ]
[ "M2437", "N0964" ]
N. J. A. Sloane
2024-09-02T08:36:43
oeisdata/seq/A002/A002821.seq
8bca669981ae4ee6ca9ad2578bdef8d7
A002822
Numbers m such that 6m-1, 6m+1 are twin primes.
[ "1", "2", "3", "5", "7", "10", "12", "17", "18", "23", "25", "30", "32", "33", "38", "40", "45", "47", "52", "58", "70", "72", "77", "87", "95", "100", "103", "107", "110", "135", "137", "138", "143", "147", "170", "172", "175", "177", "182", "192", "205", "213", "215", "217", "220", "238", "242", "247", "248", "268", "270", "278", "283", "287", "298", "312", "313", "322", "325" ]
[ "nonn", "nice", "easy" ]
153
0
5
[ "A002822", "A014574", "A024898", "A024899", "A067611", "A191626", "A263282" ]
[ "M0641", "N0235" ]
N. J. A. Sloane
2023-07-31T02:48:01
oeisdata/seq/A002/A002822.seq
90622a568b42a24b9925b269babe6af9
A002823
Number of period-n solutions to a certain "universal" equation related to transformations on the unit interval.
[ "1", "1", "3", "4", "9", "14", "27", "48", "93", "163", "315", "576", "1085" ]
[ "nonn", "nice", "more" ]
24
0
5
[ "A000048", "A001372", "A002823" ]
[ "M2357", "N0933" ]
N. J. A. Sloane
2022-01-29T01:01:07
oeisdata/seq/A002/A002823.seq
a75b27a44735d62ecbc5d36f359af5ed
A002824
Number of precomplete Post functions.
[ "1", "3", "18", "190", "3285", "88851", "3640644", "220674924", "19427552055", "2448107338105", "436330306419678", "108909970814260122", "37752710546082668409", "18044326480066641231855", "11818118910855384843861960", "10549135258779933616014791704", "12772521057179994145518171256587" ]
[ "nonn" ]
41
0
5
[ "A001035", "A002824" ]
[ "M3053", "N1237" ]
N. J. A. Sloane
2023-09-30T09:18:34
oeisdata/seq/A002/A002824.seq
1fbaa5c457d77bd0314c15ed92b17edd
A002825
Number of precomplete Post functions.
[ "1", "2", "9", "40", "355", "11490", "7758205", "549758283980", "10626621620680257450759", "1701411834605079120446041612344662275078", "79607061350691085453966118726400345961810854094316840855510985234351715774913" ]
[ "nonn" ]
39
0
5
null
[ "M1935", "N0765" ]
N. J. A. Sloane
2023-09-30T13:07:55
oeisdata/seq/A002/A002825.seq
3f8297bc63e26ecb0a7f74c0db067ab2
A002826
Number of precomplete Post functions of n variables.
[ "1", "5", "18", "82", "643", "15182", "7848984", "549761932909", "10626621620680478174719", "1701411834605079120446041612364090304458", "79607061350691085453966118726400345961810854094316840855510985236799831016092" ]
[ "nonn" ]
31
0
5
[ "A002824", "A002825", "A002826", "A008827", "A246069", "A246137", "A246417" ]
[ "M3883", "N1593" ]
N. J. A. Sloane
2024-02-20T12:13:29
oeisdata/seq/A002/A002826.seq
2fef0f43df176c90c8c4701e2db32d26
A002827
Unitary perfect numbers: numbers k such that usigma(k) - k = k.
[ "6", "60", "90", "87360", "146361946186458562560000" ]
[ "nonn", "nice", "hard" ]
66
0
5
[ "A002827", "A003062", "A034448", "A034460", "A057447", "A290466", "A293188", "A327157", "A327158", "A327159" ]
[ "M4268", "N1783" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002827.seq
51576ce79b6a5a6b7ac283ca7557c6f2
A002828
Least number of squares that add up to n.
[ "0", "1", "2", "3", "1", "2", "3", "4", "2", "1", "2", "3", "3", "2", "3", "4", "1", "2", "2", "3", "2", "3", "3", "4", "3", "1", "2", "3", "4", "2", "3", "4", "2", "3", "2", "3", "1", "2", "3", "4", "2", "2", "3", "3", "3", "2", "3", "4", "3", "1", "2", "3", "2", "2", "3", "4", "3", "3", "2", "3", "4", "2", "3", "4", "1", "2", "3", "3", "2", "3", "3", "4", "2", "2", "2", "3", "3", "3", "3", "4", "2", "1", "2", "3", "3", "2", "3", "4", "3", "2", "2", "3", "4", "3", "3", "4", "3", "2", "2", "3", "1", "2", "3", "4", "2", "3" ]
[ "nonn", "nice", "changed" ]
115
0
5
[ "A000290", "A000378", "A000415", "A000419", "A001481", "A002376", "A002828", "A004215", "A010052", "A025426", "A025427", "A053610", "A062535", "A072401", "A229062", "A255131", "A260728", "A260731", "A260734", "A262678", "A262689", "A262690", "A276573" ]
[ "M0404", "N0155" ]
N. J. A. Sloane
2025-04-21T16:03:57
oeisdata/seq/A002/A002828.seq
18c65dfcc31babaf6f9ec32e28b0531e
A002829
Number of trivalent (or cubic) labeled graphs with 2n nodes.
[ "1", "0", "1", "70", "19355", "11180820", "11555272575", "19506631814670", "50262958713792825", "187747837889699887800", "976273961160363172131825", "6840300875426184026353242750", "62870315446244013091262178375075", "741227949070136911068308523257857500" ]
[ "nonn", "changed" ]
120
0
5
[ "A002829", "A004109", "A005814", "A059441" ]
[ "M5346", "N2324" ]
N. J. A. Sloane
2025-04-15T08:29:00
oeisdata/seq/A002/A002829.seq
69f43ccd17b9b1a9e95717802df9e2c1
A002830
Number of 3-edge-colored trivalent graphs with 2n nodes.
[ "1", "1", "5", "16", "86", "448", "3580", "34981", "448628", "6854130", "121173330", "2403140605", "52655943500", "1260724587515", "32726520985365", "915263580719998", "27432853858637678", "877211481667946811", "29807483816421710806", "1072542780403547030073", "40739888428757581326987" ]
[ "nonn" ]
41
0
5
[ "A002830", "A002831", "A006712", "A006713" ]
[ "M3871", "N1586" ]
N. J. A. Sloane
2023-05-03T09:14:20
oeisdata/seq/A002/A002830.seq
230efebfd08fb63dcf7e0e88454bd3ce
A002831
Number of 3-edge-colored connected trivalent graphs with 2n nodes.
[ "1", "4", "11", "60", "318", "2806", "29359", "396196", "6231794", "112137138", "2249479114", "49691965745", "1197158348160", "31230408793660", "876971159096883", "26374570956403684", "845812191249484022", "28812214090645864661", "1038982259432805270094", "39540452134474760212909" ]
[ "nonn" ]
83
0
5
[ "A002830", "A002831", "A006712", "A006713" ]
[ "M3424", "N1388" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002831.seq
e4998caa34cd0820c8867f4367a063be
A002832
Median Euler numbers.
[ "1", "3", "24", "402", "11616", "514608", "32394624", "2748340752", "302234850816", "41811782731008", "7106160248346624", "1455425220196234752", "353536812021243273216", "100492698847094242603008", "33045185784774350171111424" ]
[ "nonn" ]
70
0
5
[ "A000657", "A002832", "A098277", "A323833" ]
null
N. J. A. Sloane, Dec 11 1996
2021-08-02T14:37:48
oeisdata/seq/A002/A002832.seq
4b5753dc956600ef2cc0c885a7fdd089
A002833
Number of threshold functions of n variables.
[ "0", "1", "2", "8", "44", "490", "14074", "1349228" ]
[ "nonn", "nice", "more" ]
18
0
5
null
[ "M1869", "N0741" ]
N. J. A. Sloane
2022-06-17T03:18:29
oeisdata/seq/A002/A002833.seq
23d3e105a289bf0dffb47022bbdac651
A002834
Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, nothing in a 3-card poker hand.
[ "48", "0", "0", "1096", "720", "52", "0", "3744", "16440" ]
[ "fini", "nonn", "full" ]
11
0
5
null
null
Luigi Barone (luigi(AT)cs.uwa.edu.au)
2011-07-10T18:39:04
oeisdata/seq/A002/A002834.seq
89a60dce6ef6e9359cf93b9bc128e346
A002835
Solid partitions of n which are restricted to two planes.
[ "1", "1", "4", "9", "22", "46", "102", "206", "427", "841", "1658", "3173", "6038", "11251", "20807", "37907", "68493", "122338", "216819", "380637", "663417", "1147033", "1969961", "3359677", "5694592", "9592063", "16065593", "26756430", "44328414" ]
[ "nonn" ]
18
0
5
[ "A000293", "A002835" ]
[ "M3363", "N1355" ]
N. J. A. Sloane
2023-09-29T22:04:31
oeisdata/seq/A002/A002835.seq
4ac8b0220adf876792fe59a0c6bd324f
A002836
Let F(x) = 1 + x + 4x^2 + 10x^3 + ... = g.f. for A000293 (solid partitions) and expand (1-x)(1-x^2)(1-x^3)...*F(x) in powers of x.
[ "1", "0", "2", "5", "12", "24", "56", "113", "248", "503", "1043", "2080", "4169", "8145", "15897", "30545", "58402", "110461", "207802", "387561", "718875", "1324038", "2425473", "4416193", "7999516", "14411507", "25837198", "46092306", "81851250", "144691532", "254682865", "446399687", "779302305" ]
[ "nonn" ]
36
0
5
[ "A000041", "A000293", "A002836", "A005980", "A161564" ]
[ "M1408", "N0550" ]
N. J. A. Sloane
2017-10-12T12:38:19
oeisdata/seq/A002/A002836.seq
89182561c1a18868f96bc9a969a4a296
A002837
Numbers k such that k^2 - k + 41 is prime.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "43", "44", "46", "47", "48", "49", "51", "52", "53", "54", "55", "56", "58", "59", "60", "61", "62", "63", "64", "65", "67", "68", "69", "70", "71", "72" ]
[ "nonn", "nice", "easy" ]
58
0
5
[ "A002837", "A007634", "A056561", "A060566" ]
[ "M0473", "N0174" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002837.seq
5d5761fbbba5ab27d47330614710d12c
A002838
Balancing weights on the integer line.
[ "1", "2", "5", "12", "32", "94", "289", "910", "2934", "9686", "32540", "110780", "381676", "1328980", "4669367", "16535154", "58965214", "211591218", "763535450", "2769176514", "10089240974", "36912710568", "135565151486", "499619269774", "1847267563742", "6850369296298" ]
[ "nonn", "easy", "nice" ]
31
0
5
[ "A002838", "A047997", "A076822", "A188181" ]
[ "M1419", "N0556" ]
N. J. A. Sloane
2022-02-20T07:15:33
oeisdata/seq/A002/A002838.seq
155a8a2e69ec45d38efc5b7d7629bf50
A002839
Number of simple perfect squared rectangles of order n up to symmetry.
[ "0", "0", "0", "0", "0", "0", "0", "0", "2", "6", "22", "67", "213", "744", "2609", "9016", "31426", "110381", "390223", "1383905", "4931308", "17633773", "63301427", "228130926", "825229110", "2994833854" ]
[ "nonn", "nice", "hard", "more" ]
133
0
5
[ "A002839", "A002881", "A002962", "A006983", "A181735", "A217153", "A217154", "A217156", "A219766" ]
[ "M1658", "N0650" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002839.seq
a2aa308777534785fd5b9fbc74c2605d
A002840
Number of polyhedral graphs with n edges.
[ "1", "0", "1", "2", "2", "4", "12", "22", "58", "158", "448", "1342", "4199", "13384", "43708", "144810", "485704", "1645576", "5623571", "19358410", "67078828", "233800162", "819267086", "2884908430", "10204782956", "36249143676", "129267865144", "462669746182", "1661652306539", "5986979643542" ]
[ "nonn", "nice" ]
45
0
5
[ "A000944", "A002840", "A002841", "A046091", "A049337", "A338511", "A343869", "A343871" ]
[ "M0339", "N0129" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002840.seq
8dbb12e308ff457bf73b164a7f9c87a0
A002841
Number of 3-connected self-dual planar graphs with 2n edges.
[ "1", "1", "2", "6", "16", "50", "165", "554", "1908", "6667", "23556", "84048", "302404", "1095536", "3993623" ]
[ "nonn", "nice", "more" ]
42
0
5
[ "A000944", "A002841" ]
[ "M1615", "N0631" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002841.seq
dcc314b09bf30eba47105d29605c0936
A002842
Number of strongly asymmetric sequences of length n.
[ "4", "12", "36", "96", "264", "648", "1584", "3576", "7872", "15360", "29184", "51120", "90384", "158448", "286296", "509808", "904296", "1556304", "2638368", "4273512", "6783888", "10308576", "15419640", "22305840", "32204568", "45812088", "65912784", "94069080" ]
[ "nonn" ]
19
0
5
null
[ "M3446", "N1400" ]
N. J. A. Sloane
2023-09-29T22:05:16
oeisdata/seq/A002/A002842.seq
d466ccea848ac71d46d5f92348baf991
A002843
Number of partitions of n into parts 1/2, 3/4, 7/8, 15/16, etc.
[ "1", "1", "2", "4", "7", "13", "24", "43", "78", "141", "253", "456", "820", "1472", "2645", "4749", "8523", "15299", "27456", "49267", "88407", "158630", "284622", "510683", "916271", "1643963", "2949570", "5292027", "9494758", "17035112", "30563634", "54835835", "98383803", "176515310", "316694823", "568197628", "1019430782" ]
[ "nonn", "nice" ]
61
0
5
[ "A002843", "A047913", "A049286" ]
[ "M1072", "N0405" ]
N. J. A. Sloane
2024-01-15T12:02:23
oeisdata/seq/A002/A002843.seq
8a61229e5ada862b41e5dcb4bdd3fb79
A002844
Number of non-isentropic binary rooted trees with n nodes.
[ "1", "1", "2", "5", "13", "36", "102", "296", "871", "2599", "7830", "23799", "72855", "224455", "695303", "2164491" ]
[ "nonn", "more" ]
48
0
5
[ "A002844", "A036765" ]
[ "M1445", "N0571" ]
N. J. A. Sloane
2023-09-29T05:41:51
oeisdata/seq/A002/A002844.seq
f29b8a2812c304f911c6daff6616da01
A002845
Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways).
[ "1", "1", "1", "2", "4", "8", "17", "36", "78", "171", "379", "851", "1928", "4396", "10087", "23273", "53948", "125608", "293543", "688366", "1619087", "3818818", "9029719", "21400706", "50828664", "120963298", "288405081", "688821573", "1647853491", "3948189131", "9473431479" ]
[ "nonn", "nice", "more" ]
87
0
5
[ "A000081", "A002845", "A003018", "A003019", "A145545", "A145546", "A145547", "A145548", "A145549", "A145550" ]
[ "M1139", "N0435" ]
N. J. A. Sloane
2024-04-28T21:55:39
oeisdata/seq/A002/A002845.seq
757dbe3d333c0c2c98c3e8c84b4bd97f
A002846
Number of ways of transforming a set of n indistinguishable objects into n singletons via a sequence of n-1 refinements.
[ "1", "1", "1", "2", "4", "11", "33", "116", "435", "1832", "8167", "39700", "201785", "1099449", "6237505", "37406458", "232176847", "1513796040", "10162373172", "71158660160", "511957012509", "3819416719742", "29195604706757", "230713267586731", "1861978821637735", "15484368121967620", "131388840051760458" ]
[ "nonn", "nice" ]
72
0
5
[ "A002846", "A213242", "A213385", "A213427", "A327643" ]
[ "M1251", "N0478" ]
N. J. A. Sloane. Entry revised by N. J. A. Sloane, Jun 11 2012
2019-09-23T10:10:52
oeisdata/seq/A002/A002846.seq
17de67520c2a8f02cddd851c6a2ec11b
A002847
Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, no pair in poker.
[ "40", "624", "3744", "5108", "10200", "54912", "123552", "1098240", "1302540" ]
[ "fini", "nonn", "full", "nice" ]
16
0
5
null
null
N. J. A. Sloane, Luigi Barone (luigi(AT)cs.uwa.edu.au)
2022-12-19T12:22:54
oeisdata/seq/A002/A002847.seq
eaa494ee6410e7b06eee86031b367ca2
A002848
Number of maximal collections of pairwise disjoint subsets {X,Y,Z} of {1, 2, ..., n} with X + Y = Z (as in A002849), with the property that n is in one of the subsets.
[ "0", "0", "0", "1", "1", "2", "2", "3", "7", "15", "12", "30", "8", "32", "164", "21", "114", "867", "3226", "720", "4414", "24412", "4079", "31454", "3040", "25737", "252727", "20505", "191778", "2140186", "14554796", "1669221", "17754992", "148553131", "14708525", "177117401", "10567748", "138584026", "1953134982", "103372655", "1431596750", "22374792451", "218018425976", "16852166906", "254094892254" ]
[ "nonn" ]
55
0
5
[ "A002848", "A002849", "A108235", "A161826" ]
[ "M0295", "N0106" ]
N. J. A. Sloane
2023-07-06T20:41:39
oeisdata/seq/A002/A002848.seq
615860cb4051eaa255cb0631c0d8a533
A002849
Number of maximal collections of pairwise disjoint subsets {X,Y,Z} of {1, 2, ..., n}, each satisfying X + Y = Z.
[ "1", "1", "1", "2", "4", "6", "3", "10", "25", "12", "42", "8", "40", "204", "21", "135", "1002", "4228", "720", "5134", "29546", "4079", "35533", "3040", "28777", "281504", "20505", "212283", "2352469", "16907265", "1669221", "19424213", "167977344", "14708525", "191825926", "10567748", "149151774", "2102286756", "103372655", "1534969405" ]
[ "nonn" ]
87
0
5
[ "A002848", "A002849", "A108235", "A161826" ]
[ "M0980", "N0368" ]
N. J. A. Sloane
2023-10-29T01:48:05
oeisdata/seq/A002/A002849.seq
c39f05dd35ab14806fcae3b01c20b5b4
A002850
Number of decompositions of 2n into sum of 2 lucky numbers.
[ "1", "1", "1", "1", "2", "1", "2", "3", "2", "1", "3", "2", "2", "3", "2", "2", "4", "2", "3", "4", "2", "3", "5", "1", "4", "5", "2", "3", "5", "1", "3", "5", "3", "3", "5", "3", "5", "7", "3", "5", "7", "4", "4", "7", "3", "3", "7", "4", "3", "9", "5", "3", "7", "5", "3", "8", "5", "4", "8", "5", "3", "7", "5", "3", "9", "4", "3", "12", "6", "4", "12", "6", "4", "10", "6", "4", "8", "5", "5", "8", "7", "5", "11", "5", "4" ]
[ "nonn", "easy", "nice" ]
32
0
5
[ "A000959", "A002850" ]
[ "M0071", "N0023" ]
N. J. A. Sloane
2022-08-03T08:55:08
oeisdata/seq/A002/A002850.seq
b31c10ee3f21133a67c72d5bbe039cf7
A002851
Number of unlabeled trivalent (or cubic) connected simple graphs with 2n nodes.
[ "1", "0", "1", "2", "5", "19", "85", "509", "4060", "41301", "510489", "7319447", "117940535", "2094480864", "40497138011", "845480228069", "18941522184590", "453090162062723", "11523392072541432", "310467244165539782", "8832736318937756165" ]
[ "nonn", "nice" ]
125
0
5
[ "A000421", "A002851", "A004109", "A005177", "A005638", "A005964", "A005967", "A006820", "A006821", "A006822", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A014377", "A014378", "A014381", "A014382", "A014384", "A068934", "A165653", "A185131", "A198303", "A275744", "A321305", "A361407" ]
[ "M1521", "N0595" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002851.seq
28aaa7bc0628491a3fad127d3226f1cf
A002852
Continued fraction for Euler's constant (or Euler-Mascheroni constant) gamma.
[ "0", "1", "1", "2", "1", "2", "1", "4", "3", "13", "5", "1", "1", "8", "1", "2", "4", "1", "1", "40", "1", "11", "3", "7", "1", "7", "1", "1", "5", "1", "49", "4", "1", "65", "1", "4", "7", "11", "1", "399", "2", "1", "3", "2", "1", "2", "1", "5", "3", "2", "1", "10", "1", "1", "1", "1", "2", "1", "1", "3", "1", "4", "1", "1", "2", "5", "1", "3", "6", "2", "1", "2", "1", "1", "1", "2", "1", "3", "16", "8", "1", "1", "2", "16", "6", "1", "2", "2", "1", "7", "2", "1", "1", "1", "3", "1", "2", "1", "2" ]
[ "nonn", "cofr", "nice" ]
87
0
5
[ "A001620", "A002852", "A033091", "A033092", "A033149", "A073004", "A094640" ]
[ "M0097", "N0034" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002852.seq
05303f634050eb886f822c43b435189e
A002853
Maximal size of a set of equiangular lines in n dimensions.
[ "1", "3", "6", "6", "10", "16", "28", "28", "28", "28", "28", "28", "28", "28", "36", "40", "48" ]
[ "nonn", "nice", "hard", "more" ]
117
0
5
[ "A002853", "A332546" ]
[ "M2514", "N0994" ]
N. J. A. Sloane
2023-09-12T09:47:14
oeisdata/seq/A002/A002853.seq
4bf228d7f0cf1223a173837223f34234
A002854
Number of unlabeled Euler graphs with n nodes; number of unlabeled two-graphs with n nodes; number of unlabeled switching classes of graphs with n nodes; number of switching classes of unlabeled signed complete graphs on n nodes; number of Seidel matrices of order n.
[ "1", "1", "2", "3", "7", "16", "54", "243", "2038", "33120", "1182004", "87723296", "12886193064", "3633057074584", "1944000150734320", "1967881448329407496", "3768516017219786199856", "13670271807937483065795200", "94109042015724412679233018144", "1232069666043220685614640133362240" ]
[ "nonn", "easy", "nice" ]
159
0
5
[ "A000666", "A002854", "A003049", "A007127", "A085618", "A085619", "A085620", "A133736", "A182012", "A182055", "A341941" ]
[ "M0846", "N0321" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002854.seq
7131592e8ee95a9fc0e50f09ad04c91b
A002855
{m + n: m in A002382, n in A002381}.
[ "0", "1", "2", "3", "4", "5", "7", "8", "9", "10", "11", "12", "14", "15", "16", "18", "19", "21", "22", "23", "24", "25", "26", "29", "30", "31", "32", "33", "35", "37", "38", "40", "42", "43", "44", "45", "46", "47", "49", "51", "52", "53", "54", "56", "57", "58", "60", "63", "64", "65", "66", "67", "68", "70", "71", "73", "75", "77", "78", "79", "81", "84", "85", "86", "87", "88", "89", "91", "92", "95", "96", "98", "99", "100" ]
[ "nonn" ]
15
0
5
[ "A002381", "A002382", "A002855" ]
[ "M0513", "N0183" ]
N. J. A. Sloane
2023-09-29T22:05:43
oeisdata/seq/A002/A002855.seq
8c2a2391d4153b515147b724db6e5f62
A002856
Number of polyhedra with n nodes and n faces.
[ "1", "1", "2", "8", "42", "296", "2635", "25626", "268394", "2937495", "33310550", "388431688", "4637550072", "56493493990", "700335433295" ]
[ "nonn", "hard", "more", "nice" ]
19
0
5
[ "A002856", "A212438" ]
[ "M1864", "N0739" ]
N. J. A. Sloane
2022-01-29T01:00:47
oeisdata/seq/A002/A002856.seq
9f5cf5360f7e9f5bff08c7f496e22d04
A002857
Number of Post functions of n variables.
[ "1", "3", "20", "996", "9333312", "6406603084568576", "16879085743296493582043922521915392", "717956902513121252476003434439730211917452457474409186632352788205535232" ]
[ "nonn" ]
37
0
5
[ "A000612", "A002857", "A003180" ]
[ "M3078", "N1249" ]
N. J. A. Sloane
2023-09-30T10:50:01
oeisdata/seq/A002/A002857.seq
7743077c32e6d16db4a792bd6458929e
A002858
Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.
[ "1", "2", "3", "4", "6", "8", "11", "13", "16", "18", "26", "28", "36", "38", "47", "48", "53", "57", "62", "69", "72", "77", "82", "87", "97", "99", "102", "106", "114", "126", "131", "138", "145", "148", "155", "175", "177", "180", "182", "189", "197", "206", "209", "219", "221", "236", "238", "241", "243", "253", "258", "260", "273", "282", "309", "316", "319", "324", "339" ]
[ "nonn", "nice" ]
271
0
5
[ "A001857", "A002858", "A002859", "A003667", "A004280", "A007300", "A033629", "A054540", "A072540", "A072832", "A080287", "A080288", "A080573", "A117140", "A199016", "A199017", "A214603", "A274522", "A285884" ]
[ "M0557", "N0201" ]
N. J. A. Sloane
2025-03-12T08:19:24
oeisdata/seq/A002/A002858.seq
024340e89c009573f1c7374b47948d21
A002859
a(1) = 1, a(2) = 3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.
[ "1", "3", "4", "5", "6", "8", "10", "12", "17", "21", "23", "28", "32", "34", "39", "43", "48", "52", "54", "59", "63", "68", "72", "74", "79", "83", "98", "99", "101", "110", "114", "121", "125", "132", "136", "139", "143", "145", "152", "161", "165", "172", "176", "187", "192", "196", "201", "205", "212", "216", "223", "227", "232", "234", "236", "243", "247", "252", "256", "258" ]
[ "nonn", "nice" ]
45
0
5
[ "A002858", "A002859", "A199118", "A199119" ]
[ "M2303", "N0909" ]
N. J. A. Sloane, Mira Bernstein
2025-02-16T08:32:27
oeisdata/seq/A002/A002859.seq
ac1fa9927c71003ad1818b2fca005f87
A002860
Number of Latin squares of order n; or labeled quasigroups.
[ "1", "2", "12", "576", "161280", "812851200", "61479419904000", "108776032459082956800", "5524751496156892842531225600", "9982437658213039871725064756920320000", "776966836171770144107444346734230682311065600000" ]
[ "hard", "nonn", "nice" ]
127
0
5
[ "A000315", "A000479", "A002860", "A003090", "A040082", "A057991", "A098679", "A249026" ]
[ "M2051", "N0812" ]
N. J. A. Sloane
2024-03-02T21:08:32
oeisdata/seq/A002/A002860.seq
d956910f823520149352036772a9d984
A002861
Number of connected functions (or mapping patterns) on n unlabeled points, or number of rings and branches with n edges.
[ "1", "2", "4", "9", "20", "51", "125", "329", "862", "2311", "6217", "16949", "46350", "127714", "353272", "981753", "2737539", "7659789", "21492286", "60466130", "170510030", "481867683", "1364424829", "3870373826", "10996890237", "31293083540", "89173833915", "254445242754", "726907585652", "2079012341822" ]
[ "nonn", "nice" ]
74
0
5
[ "A000081", "A001372", "A002861", "A027852", "A029852", "A029853", "A029868", "A339428" ]
[ "M1182", "N0455" ]
N. J. A. Sloane
2025-02-10T04:38:31
oeisdata/seq/A002/A002861.seq
cea277de0a777e443634691137a3b962
A002862
Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges.
[ "0", "1", "2", "5", "11", "31", "77", "214", "576", "1592", "4375", "12183", "33864", "94741", "265461", "746372", "2102692", "5938630", "16803610", "47639902", "135288198", "384812502", "1096141974", "3126648842", "8929715592", "25533447030", "73090099586", "209438176485", "600721031344", "1724585494225" ]
[ "nonn", "nice" ]
35
0
5
[ "A000081", "A002861", "A002862" ]
[ "M1403", "N0547" ]
N. J. A. Sloane
2017-10-02T02:14:09
oeisdata/seq/A002/A002862.seq
9e55dae2e656b3632c8f2e3d506e238c
A002863
Number of prime knots with n crossings.
[ "0", "0", "1", "1", "2", "3", "7", "21", "49", "165", "552", "2176", "9988", "46972", "253293", "1388705", "8053393", "48266466", "294130458" ]
[ "nonn", "hard", "more", "nice" ]
185
0
5
[ "A002863", "A002864", "A051766", "A051767", "A051768", "A051769", "A052400", "A086825" ]
[ "M0851", "N0323" ]
N. J. A. Sloane
2025-04-05T10:57:38
oeisdata/seq/A002/A002863.seq
a3e1a4e1a588a1454aa1b4c331c48573
A002864
Number of alternating prime knots with n crossings.
[ "0", "0", "1", "1", "2", "3", "7", "18", "41", "123", "367", "1288", "4878", "19536", "85263", "379799", "1769979", "8400285", "40619385", "199631989", "990623857", "4976016485", "25182878921", "128564665125" ]
[ "nonn", "hard", "more", "nice" ]
64
0
5
[ "A002863", "A002864", "A049344", "A059739" ]
[ "M0847", "N0322" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002864.seq
c19405190e3b8350301a452232c0db45
A002865
Number of partitions of n that do not contain 1 as a part.
[ "1", "0", "1", "1", "2", "2", "4", "4", "7", "8", "12", "14", "21", "24", "34", "41", "55", "66", "88", "105", "137", "165", "210", "253", "320", "383", "478", "574", "708", "847", "1039", "1238", "1507", "1794", "2167", "2573", "3094", "3660", "4378", "5170", "6153", "7245", "8591", "10087", "11914", "13959", "16424", "19196", "22519", "26252", "30701" ]
[ "nonn", "easy", "nice" ]
324
0
5
[ "A000041", "A002033", "A002865", "A008483", "A008484", "A025147", "A027336", "A053445", "A058682", "A070003", "A072380", "A081094", "A081095", "A085811", "A090824", "A098743", "A103295", "A133687", "A145573", "A147768", "A171239", "A185325", "A185329", "A229161", "A232697", "A247180", "A274161", "A292508", "A292622", "A325676", "A325684", "A325761", "A325762", "A325763" ]
[ "M0309", "N0113" ]
N. J. A. Sloane
2024-12-03T12:31:52
oeisdata/seq/A002/A002865.seq
515654f470653adfd48d80e055d88f4d
A002866
a(0) = 1; for n > 0, a(n) = 2^(n-1)*n!.
[ "1", "1", "4", "24", "192", "1920", "23040", "322560", "5160960", "92897280", "1857945600", "40874803200", "980995276800", "25505877196800", "714164561510400", "21424936845312000", "685597979049984000", "23310331287699456000", "839171926357180416000", "31888533201572855808000", "1275541328062914232320000" ]
[ "nonn", "easy", "nice" ]
209
0
5
[ "A002671", "A002866", "A028371", "A078602", "A078698", "A078702", "A156992", "A167584", "A167594", "A274304" ]
[ "M3604", "N1463" ]
N. J. A. Sloane
2025-02-01T23:16:35
oeisdata/seq/A002/A002866.seq
d50a115a3ec093427de1930229377de8
A002867
a(n) = binomial(n,floor(n/2))*(n+1)!.
[ "1", "2", "12", "72", "720", "7200", "100800", "1411200", "25401600", "457228800", "10059033600", "221298739200", "5753767219200", "149597947699200", "4487938430976000", "134638152929280000", "4577697199595520000", "155641704786247680000" ]
[ "nonn", "easy" ]
43
0
5
[ "A000246", "A002867" ]
[ "M2035", "N0806" ]
N. J. A. Sloane
2018-09-04T16:58:41
oeisdata/seq/A002/A002867.seq
f858a11e632337e79a4cb4714444276e
A002868
Largest number in n-th row of triangle of Lah numbers (A008297 and A271703).
[ "1", "1", "2", "6", "36", "240", "1800", "15120", "141120", "1693440", "21772800", "299376000", "4390848000", "68497228800", "1133317785600", "19833061248000", "396661224960000", "8299373322240000", "181400588328960000", "4135933413900288000", "98228418580131840000", "2426819753156198400000" ]
[ "nonn", "nice", "easy" ]
50
0
5
[ "A000262", "A001286", "A002868", "A008297", "A105278", "A271703" ]
[ "M1703", "N0673" ]
N. J. A. Sloane
2019-10-21T16:20:03
oeisdata/seq/A002/A002868.seq
fec25924edbe219f950fbb70d0b6f344
A002869
Largest number in n-th row of triangle A019538.
[ "1", "1", "2", "6", "36", "240", "1800", "16800", "191520", "2328480", "30240000", "479001600", "8083152000", "142702560000", "2731586457600", "59056027430400", "1320663933388800", "30575780537702400", "783699448602470400", "21234672840116736000", "591499300737945600000" ]
[ "nonn", "nice", "easy" ]
49
0
5
[ "A000670", "A002869", "A019538", "A058583", "A131689" ]
[ "M1704", "N0674" ]
N. J. A. Sloane
2024-10-24T12:33:42
oeisdata/seq/A002/A002869.seq
c97dcea11c86b510628c4d05e4ad36de
A002870
Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
[ "1", "1", "3", "7", "25", "90", "350", "1701", "7770", "42525", "246730", "1379400", "9321312", "63436373", "420693273", "3281882604", "25708104786", "197462483400", "1709751003480", "15170932662679", "132511015347084", "1241963303533920", "12320068811796900", "120622574326072500", "1203163392175387500" ]
[ "nonn", "nice", "easy" ]
43
0
5
[ "A002870", "A008277", "A024417" ]
[ "M2690", "N1077" ]
N. J. A. Sloane
2020-05-01T02:40:24
oeisdata/seq/A002/A002870.seq
f3a849f7e6134d32e74e5177b2488dc4
A002871
a(n) = max_{k=0..n} 2^k*A048993(n,k).
[ "1", "2", "4", "12", "48", "200", "1040", "5600", "33600", "222432", "1460928", "11487168", "84713728", "731574272", "6314147840", "55456727040", "548291597568", "5226494727168", "54361802626560", "586042688924160", "6149776714099200", "72895623466265600", "855187250563024896" ]
[ "nonn", "nice" ]
55
0
5
[ "A002871", "A008277", "A048993", "A227450" ]
[ "M1261", "N0483" ]
N. J. A. Sloane
2025-01-18T02:20:09
oeisdata/seq/A002/A002871.seq
f68b710e73d8dcbb53e8b9977a43fe36
A002872
Number of partitions of {1..2n} that are invariant under a permutation consisting of n 2-cycles.
[ "1", "2", "7", "31", "164", "999", "6841", "51790", "428131", "3827967", "36738144", "376118747", "4086419601", "46910207114", "566845074703", "7186474088735", "95318816501420", "1319330556537631", "19013488408858761", "284724852032757686", "4422344774431494155", "71125541977466879231" ]
[ "nonn", "easy", "nice" ]
123
0
5
[ "A002872", "A002873", "A002874", "A005425", "A080107", "A085483", "A162663", "A293181", "A306024" ]
[ "M1786", "N0705" ]
N. J. A. Sloane, Simon Plouffe
2025-02-01T08:24:39
oeisdata/seq/A002/A002872.seq
5e6d12446a16f54dc35172231949bf57
A002873
The maximal number of partitions of {1..2n} that are invariant under a permutation consisting of n 2-cycles, and which have the same number of nonempty parts.
[ "1", "1", "3", "10", "53", "265", "1700", "13097", "96796", "829080", "8009815", "75604892", "808861988", "9175286549", "106167118057", "1320388106466", "16950041305210", "233232366601078", "3243603207488124", "47776065074368313", "733990397879859192", "11515503147927664816", "189107783918416912912" ]
[ "nonn", "nice" ]
68
0
5
[ "A000262", "A002872", "A002873", "A293181" ]
[ "M2872", "N1154" ]
N. J. A. Sloane
2018-04-24T16:52:44
oeisdata/seq/A002/A002873.seq
79c0c46ae9a6acf576e5936de588b47b
A002874
The number of partitions of {1..3n} that are invariant under a permutation consisting of n 3-cycles.
[ "1", "2", "8", "42", "268", "1994", "16852", "158778", "1644732", "18532810", "225256740", "2933174842", "40687193548", "598352302474", "9290859275060", "151779798262202", "2600663778494172", "46609915810749130", "871645673599372868", "16971639450858467002", "343382806080459389676" ]
[ "nonn", "easy", "nice" ]
82
0
5
[ "A000110", "A002872", "A002874", "A036075", "A036077", "A141003", "A141004", "A162663", "A294201" ]
[ "M1863", "N0738" ]
N. J. A. Sloane, Simon Plouffe
2025-02-01T08:22:58
oeisdata/seq/A002/A002874.seq
a9aad684f437ae8bea1e31380f438e09
A002875
Sorting numbers (see Motzkin article for details).
[ "1", "2", "4", "24", "128", "880", "7440" ]
[ "nonn", "unkn", "more" ]
41
0
5
[ "A000262", "A001861", "A002872", "A002873", "A002874", "A002875", "A036073", "A294201", "A294202" ]
[ "M1300", "N0498" ]
N. J. A. Sloane
2017-10-28T09:52:17
oeisdata/seq/A002/A002875.seq
5379ad818ee5cda39cf804a14a2743b8
A002876
Number of weighted linear spaces of total weight n.
[ "1", "2", "4", "8", "16", "36", "85", "239" ]
[ "nonn", "nice", "more" ]
15
0
5
[ "A001200", "A002876", "A002877" ]
[ "M1136", "N0433" ]
N. J. A. Sloane
2022-01-29T01:00:17
oeisdata/seq/A002/A002876.seq
a637ede17d3cd1cdc167ec71d54356bd
A002877
Number of connected weighted linear spaces of total weight n.
[ "1", "1", "2", "3", "6", "13", "35", "116" ]
[ "nonn", "hard", "nice", "more" ]
16
0
5
[ "A001200", "A002876", "A002877" ]
[ "M0802", "N0304" ]
N. J. A. Sloane
2022-01-29T01:00:24
oeisdata/seq/A002/A002877.seq
ddaf49140f8128454a9e7085308ee065
A002878
Bisection of Lucas sequence: a(n) = L(2*n+1).
[ "1", "4", "11", "29", "76", "199", "521", "1364", "3571", "9349", "24476", "64079", "167761", "439204", "1149851", "3010349", "7881196", "20633239", "54018521", "141422324", "370248451", "969323029", "2537720636", "6643838879", "17393796001", "45537549124", "119218851371", "312119004989", "817138163596", "2139295485799" ]
[ "nonn", "easy", "changed" ]
408
0
5
[ "A000045", "A000204", "A001906", "A002315", "A002878", "A004146", "A005248", "A029907", "A060923", "A081071", "A113224", "A153387", "A153416", "A178482", "A192425", "A264080", "A285992" ]
[ "M3420", "N1384" ]
N. J. A. Sloane
2025-04-19T06:13:39
oeisdata/seq/A002/A002878.seq
0179d1036cc96dbdc7ca64f8cb160f79
A002879
Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, nothing in a 7-card poker hand.
[ "41584", "224848", "3473184", "4047644", "6180020", "6461620", "31433400", "58627800", "23294460" ]
[ "fini", "nonn", "full" ]
40
0
5
null
null
Luigi Barone (luigi(AT)cs.uwa.edu.au)
2019-08-23T04:07:50
oeisdata/seq/A002/A002879.seq
c9c85ebf4a0a849a2c90fca60528bb4f
A002880
Number of 3-connected nets with n edges.
[ "1", "0", "1", "1", "2", "2", "9", "11", "37", "79", "249", "671", "2182", "6692", "22131", "72405", "243806", "822788", "2815119", "9679205", "33551192", "116900081", "409675567", "1442454215", "5102542680", "18124571838", "64634480340", "231334873091", "830828150081", "2993489821771" ]
[ "nonn", "nice" ]
49
0
5
[ "A002840", "A002841", "A002880", "A007022", "A078666", "A113201", "A113205", "A338511" ]
[ "M0381", "N0143" ]
N. J. A. Sloane
2023-11-07T20:42:57
oeisdata/seq/A002/A002880.seq
5fdebae1cfb68f5f6a244a04157ca592
A002881
Number of simple imperfect squared rectangles of order n up to symmetry.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "9", "34", "104", "283", "953", "3029", "9513", "30359", "98969", "323646", "1080659", "3668432", "12608491", "43745771", "153812801" ]
[ "hard", "nonn" ]
58
0
5
[ "A002839", "A002881", "A002962", "A006983", "A181735", "A217153", "A217154", "A217156", "A220165" ]
[ "M4614", "N1969" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A002/A002881.seq
5e2bcd6b5392d315dc84e3f31dd18baf
A002882
Nearest integer to Bernoulli number B_{2n}.
[ "1", "0", "0", "0", "0", "0", "0", "1", "-7", "55", "-529", "6192", "-86580", "1425517", "-27298231", "601580874", "-15116315767", "429614643061", "-13711655205088", "488332318973593", "-19296579341940068", "841693047573682615", "-40338071854059455413", "2115074863808199160560", "-120866265222965259346027", "7500866746076964366855720" ]
[ "sign", "easy", "nice" ]
30
0
5
null
[ "M4435", "N1875" ]
N. J. A. Sloane
2018-05-08T15:11:53
oeisdata/seq/A002/A002882.seq
2de39ac4a7f13a207cb21fe209201d40
A002883
Number of allomorphic polyhedra with n nodes.
[ "1", "2", "5", "9", "18", "31", "57", "92", "159" ]
[ "nonn" ]
13
0
5
null
[ "M1362", "N0526" ]
N. J. A. Sloane
2023-10-20T21:32:07
oeisdata/seq/A002/A002883.seq
df1ab640109a33695c0400a6292c8a2f
A002884
Number of nonsingular n X n matrices over GF(2) (order of the group GL(n,2)); order of Chevalley group A_n (2); order of projective special linear group PSL_n(2).
[ "1", "1", "6", "168", "20160", "9999360", "20158709760", "163849992929280", "5348063769211699200", "699612310033197642547200", "366440137299948128422802227200", "768105432118265670534631586896281600", "6441762292785762141878919881400879415296000", "216123289355092695876117433338079655078664339456000" ]
[ "nonn", "easy", "nice" ]
117
0
5
[ "A000409", "A000410", "A002820", "A002884", "A005329", "A006125", "A028365", "A046747", "A048651", "A203303", "A316622", "A316623" ]
[ "M4302", "N1798" ]
N. J. A. Sloane
2025-01-10T18:27:08
oeisdata/seq/A002/A002884.seq
3fa8f2d07cfa809acf2b2e0a89fdf665
A002885
Number of cyclic Steiner triple systems of order 2n+1.
[ "1", "1", "0", "1", "0", "0", "1", "2", "0", "4", "7", "0", "12", "8", "0", "80", "84", "0", "820", "798", "0", "9508", "11616", "0", "157340", "139828", "0", "3027456", "2353310" ]
[ "nonn", "more" ]
22
0
5
null
[ "M0032", "N0393" ]
N. J. A. Sloane
2024-07-31T09:49:41
oeisdata/seq/A002/A002885.seq
f2d7fbc49a1218ba44d2349424a5dfdc
A002886
Van der Waerden numbers W(2;2,n-1).
[ "2", "6", "9", "18", "22", "32", "46", "58", "77", "97", "114", "135", "160", "186", "218" ]
[ "dead" ]
20
0
5
[ "A002886", "A007783" ]
[ "M1572", "N0614" ]
null
2024-12-27T22:38:06
oeisdata/seq/A002/A002886.seq
3300f12dd32cd87e77ff1753b16bc5fb
A002887
The minimum number of nodes of a tree with a cutting center of n nodes.
[ "3", "4", "7", "10", "50" ]
[ "nonn", "more" ]
42
0
5
[ "A002887", "A002888", "A331237" ]
[ "M2340", "N0923" ]
N. J. A. Sloane
2024-07-31T09:20:26
oeisdata/seq/A002/A002887.seq
c0fbf24cf208d0bb7f617cab7c5c1d13
A002888
a(n) is the cutting number of the tree corresponding to A002887(n).
[ "1", "2", "9", "20", "670" ]
[ "nonn", "more" ]
24
0
5
[ "A002887", "A002888", "A331237" ]
[ "M1919", "N0757" ]
N. J. A. Sloane
2024-07-31T09:14:45
oeisdata/seq/A002/A002888.seq
474fced5bd48ced68e5299d5e133ece0
A002889
Arrays of dumbbells.
[ "1", "10", "56", "234", "815", "2504", "7018", "18336", "45328", "107160", "244198", "539656", "1161987", "2446906", "5054440", "10266850", "20549117", "40595568", "79271188", "153190480", "293278496", "556737696", "1048772300", "1961855408", "3646420325", "6737649754" ]
[ "nonn", "easy" ]
35
0
5
[ "A002889", "A002940", "A002941", "A046741", "A055608", "A062123", "A062127" ]
[ "M4715", "N2016" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002889.seq
afda133df913cf5cd8833f30f9b82b8a
A002890
Low temperature series for spin-1/2 Ising partition function on 2D square lattice.
[ "1", "0", "1", "2", "5", "14", "44", "152", "566", "2234", "9228", "39520", "174271", "787246", "3628992", "17019374", "81011889", "390633382", "1905134695", "9385453576", "46653815395", "233788460256", "1180111379105", "5996452414310", "30653752894948" ]
[ "nonn" ]
60
0
5
[ "A002890", "A002891" ]
[ "M1463", "N0578" ]
N. J. A. Sloane
2024-05-02T03:52:51
oeisdata/seq/A002/A002890.seq
992445596b19d18b658c4ee530d81a38
A002891
Low temperature series for spin-1/2 Ising partition function on 3-dimensional simple cubic lattice.
[ "1", "0", "0", "1", "0", "3", "-3", "15", "-30", "101", "-261", "807", "-2308", "7065", "-21171", "65337", "-200934", "627249", "-1962034", "6192066", "-19610346", "62482527", "-199807110", "641837193", "-2068695927", "6691611633", "-21710041944", "70645706963", "-230488840446", "753903842400", "-2471624380458", "8120879664294", "-26736570257010" ]
[ "sign" ]
30
0
5
[ "A001393", "A002890", "A002891", "A002892", "A002915", "A002926", "A030045", "A030047" ]
[ "M2293", "N0906" ]
N. J. A. Sloane, C. Vohwinkel
2022-06-30T06:00:59
oeisdata/seq/A002/A002891.seq
1635ede0a2cbba28ac0cb433495f2df8
A002892
Low-temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.
[ "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "6", "-6", "0", "0", "8", "42", "-114", "66", "24", "123", "134", "-1563", "2262", "-405", "846", "-2532", "-15182", "47961", "-37992", "8044", "-59694", "-57117", "742394", "-1233840", "597456", "-798392", "1447162", "7898736", "-27134598", "27649335" ]
[ "sign" ]
29
0
5
[ "A001407", "A002891", "A002892", "A002924", "A003196" ]
[ "M4055", "N1682" ]
N. J. A. Sloane
2022-02-16T11:10:23
oeisdata/seq/A002/A002892.seq
44c4e0e4ba4f800d3600b4a175b88b8d
A002893
a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k).
[ "1", "3", "15", "93", "639", "4653", "35169", "272835", "2157759", "17319837", "140668065", "1153462995", "9533639025", "79326566595", "663835030335", "5582724468093", "47152425626559", "399769750195965", "3400775573443089", "29016970072920387", "248256043372999089" ]
[ "nonn", "easy", "walk", "nice" ]
308
0
5
[ "A000172", "A000984", "A002893", "A002895", "A005258", "A005259", "A005260", "A006077", "A006480", "A036917", "A063007", "A081085", "A087457", "A093388", "A125143", "A133370", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A169714", "A169715", "A183204", "A214262", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A274600", "A279619", "A290575", "A290576", "A291275", "A291284", "A318397" ]
[ "M2998", "N1214" ]
N. J. A. Sloane
2025-03-28T17:32:47
oeisdata/seq/A002/A002893.seq
6e92ab4ac12e7d624f29763ee5d70795
A002894
a(n) = binomial(2n, n)^2.
[ "1", "4", "36", "400", "4900", "63504", "853776", "11778624", "165636900", "2363904400", "34134779536", "497634306624", "7312459672336", "108172480360000", "1609341595560000", "24061445010950400", "361297635242552100", "5445717990022688400", "82358080713306090000", "1249287673091590440000" ]
[ "nonn", "nice", "easy", "changed" ]
274
0
5
[ "A000515", "A000894", "A000897", "A000984", "A002894", "A002897", "A002898", "A006480", "A008977", "A010370", "A054474", "A060150", "A069466", "A172390", "A186420", "A188662", "A241530", "A268367" ]
[ "M3664", "N1490" ]
N. J. A. Sloane
2025-04-15T05:44:52
oeisdata/seq/A002/A002894.seq
b6d2bbee4cedffb7cf5dcebad4eebd88
A002895
Domb numbers: number of 2n-step polygons on diamond lattice.
[ "1", "4", "28", "256", "2716", "31504", "387136", "4951552", "65218204", "878536624", "12046924528", "167595457792", "2359613230144", "33557651538688", "481365424895488", "6956365106016256", "101181938814289564", "1480129751586116848", "21761706991570726096", "321401321741959062016" ]
[ "nonn", "easy", "nice", "walk" ]
239
0
5
[ "A000172", "A000984", "A002893", "A002895", "A005258", "A005259", "A005260", "A006077", "A008459", "A036917", "A063007", "A081085", "A093388", "A125143", "A133370", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A169714", "A169715", "A183204", "A214262", "A219692", "A226535", "A227216", "A227454", "A228289", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A267219", "A279619", "A290575", "A290576", "A291275", "A291284" ]
[ "M3626", "N1473" ]
N. J. A. Sloane
2025-01-09T19:05:58
oeisdata/seq/A002/A002895.seq
22f6edf18dd349975c3a7b3f9087bf23
A002896
Number of 2n-step polygons on cubic lattice.
[ "1", "6", "90", "1860", "44730", "1172556", "32496156", "936369720", "27770358330", "842090474940", "25989269017140", "813689707488840", "25780447171287900", "825043888527957000", "26630804377937061000", "865978374333905289360", "28342398385058078078010", "932905175625150142902300" ]
[ "nonn", "easy", "walk", "nice", "changed" ]
203
0
5
[ "A002893", "A002896", "A049020", "A049037", "A084261", "A138540", "A174516", "A268545", "A268555", "A287318" ]
[ "M4285", "N1791" ]
N. J. A. Sloane
2025-04-20T03:46:16
oeisdata/seq/A002/A002896.seq
aa208412694756ba9cf369fb94990468
A002897
a(n) = binomial(2n,n)^3.
[ "1", "8", "216", "8000", "343000", "16003008", "788889024", "40424237568", "2131746903000", "114933031928000", "6306605327953216", "351047164190381568", "19774031697705428416", "1125058699232216000000", "64561313052442296000000" ]
[ "nonn", "easy" ]
117
0
5
[ "A000897", "A002894", "A002897", "A006480", "A008977", "A108625", "A176285", "A183204", "A186420", "A188662", "A268545", "A268555" ]
[ "M4580", "N1952" ]
N. J. A. Sloane, Simon Plouffe
2024-10-18T11:42:44
oeisdata/seq/A002/A002897.seq
f35b28a718dd768dffd02397fccc5876
A002898
Number of n-step closed paths on hexagonal lattice.
[ "1", "0", "6", "12", "90", "360", "2040", "10080", "54810", "290640", "1588356", "8676360", "47977776", "266378112", "1488801600", "8355739392", "47104393050", "266482019232", "1512589408044", "8610448069080", "49144928795820", "281164160225520", "1612061452900080", "9261029179733760", "53299490722049520" ]
[ "nonn", "walk", "nice" ]
116
0
5
[ "A000172", "A002893", "A002894", "A002898", "A006480", "A094060", "A337905", "A337907" ]
[ "M4101", "N1701" ]
N. J. A. Sloane
2022-04-23T01:33:33
oeisdata/seq/A002/A002898.seq
5a4888194a8e115035f673e2c012c81b
A002899
Number of n-step polygons on f.c.c. lattice.
[ "1", "0", "12", "48", "540", "4320", "42240", "403200", "4038300", "40958400", "423550512", "4434978240", "46982827584", "502437551616", "5417597053440", "58831951546368", "642874989479580", "7063600894137216", "77991775777488144", "864910651813116480" ]
[ "nonn", "walk", "nice" ]
54
0
5
[ "A002895", "A002898", "A002899" ]
[ "M4840", "N2068" ]
N. J. A. Sloane
2022-01-31T06:47:12
oeisdata/seq/A002/A002899.seq
dc626027a0442f4bd39f222e8d30c775
A002900
Number of n-step walks on square lattice.
[ "2", "6", "18", "50", "142", "390", "1086", "2958", "8134", "22050", "60146", "162466", "440750", "1187222", "3208298", "8622666", "23233338", "62329366", "167558310", "448848582", "1204403014", "3222280242", "8633306906", "23073198658", "61740677454", "164856393110", "440658745814" ]
[ "nonn", "walk" ]
36
0
5
[ "A001411", "A002900", "A046661" ]
[ "M1621", "N0634" ]
N. J. A. Sloane
2019-12-27T17:46:50
oeisdata/seq/A002/A002900.seq
84e5ba48b2505f0e39eac0439db455e9