cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A373870 a(n) = Sum_{k=1..n} k! * k^(n-3) * |Stirling1(n,k)|.

Original entry on oeis.org

0, 1, 2, 14, 254, 9154, 552034, 50183832, 6417140232, 1098719459424, 242758470248976, 67260880064331216, 22840933997866565184, 9330599517868641290160, 4514326567036815466609008, 2553018492454631240215801344, 1668797317379516060093446975104
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k!*k^(n-3)*abs(stirling(n, k, 1)));

Formula

E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k^3.

A373871 a(n) = Sum_{k=1..n} k! * k^(n-3) * Stirling2(n,k).

Original entry on oeis.org

0, 1, 2, 13, 233, 8311, 495437, 44495263, 5619239453, 949995402271, 207228784973597, 56681221280785663, 19000392210559326173, 7661410911700580500831, 3658694812581483750630557, 2042247041839449013948374463, 1317554928647608644852032652893
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k!*k^(n-3)*stirling(n, k, 2));

Formula

E.g.f.: Sum_{k>=1} (exp(k*x) - 1)^k / k^3.

A373872 a(n) = Sum_{k=1..n} (-1)^(n-k) * k! * k^(n-3) * Stirling2(n,k).

Original entry on oeis.org

0, 1, 0, 1, 15, 391, 16275, 999391, 85314915, 9682617631, 1411532175075, 257220473522431, 57317980108103715, 15338554965273810271, 4855172557420679314275, 1794588990417909081447871, 766066194581899382513514915, 374061220058388896558805473311
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, (-1)^(n-k)*k!*k^(n-3)*stirling(n, k, 2));

Formula

E.g.f.: Sum_{k>=1} (1 - exp(-k*x))^k / k^3.
Sum_{k>=0} a(k+2) * x^k/k! = Sum_{k>=0} k * (1 - exp(-k*x))^k.

A373874 a(n) = Sum_{k=1..n} k! * k^(n-2) * Stirling1(n,k).

Original entry on oeis.org

0, 1, 1, 8, 142, 4534, 229658, 16951416, 1718394312, 229119947280, 38881745126112, 8183542269446928, 2092128552508587360, 638590833851037194256, 229398149222697428624688, 95801846241560025353728512, 46025711723325944648182502016
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k!*k^(n-2)*stirling(n, k, 1));

Formula

E.g.f.: Sum_{k>=1} log(1 + k*x)^k / k^2.
Showing 1-4 of 4 results.