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 1-3 of 3 results.

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.

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.

A373875 a(n) = Sum_{k=1..n} k! * k^(n-2) * |Stirling1(n,k)|.

Original entry on oeis.org

0, 1, 3, 32, 802, 36854, 2698598, 288450168, 42388536888, 8198703649296, 2019226648157472, 616991110153816848, 229048514514263311008, 101540936651344709359632, 52984383824921037875927760, 32145394332240602286960456192
Offset: 0

Views

Author

Seiichi Manyama, Jun 20 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k^2.
Showing 1-3 of 3 results.