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 1-2 of 2 results.

A354244 Expansion of e.g.f. Sum_{k>=0} (2*k)! * (-log(1-x))^k / k!.

Original entry on oeis.org

1, 2, 26, 796, 44916, 4058448, 537029616, 97903213056, 23525415709632, 7205450503530816, 2740066802232081984, 1266655419369548369280, 699532666466320784246400, 454880976674201215672273920, 344008843780994236543882521600
Offset: 0

Views

Author

Seiichi Manyama, May 20 2022

Keywords

Crossrefs

Cf. A007840, A354251.
Cf. A316747, A354241.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k)!*(-log(1-x))^k/k!)))
  • PARI
    a(n) = sum(k=0, n, (2*k)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (2*k)! * |Stirling1(n,k)|.

A354250 Expansion of e.g.f. Sum_{k>=0} (3*k)! * log(1+x)^k / k!.

Original entry on oeis.org

1, 6, 714, 360732, 476832204, 1302897016944, 6382799223892560, 50956720815425427360, 619019914356960664044960, 10866561174598537960652828160, 264763399994627082733034386813440, 8668743073576807048450006051943930880
Offset: 0

Views

Author

Seiichi Manyama, May 21 2022

Keywords

Crossrefs

Cf. A006252, A354243.
Cf. A316748, A354229, A354251.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*log(1+x)^k/k!)))
  • PARI
    a(n) = sum(k=0, n, (3*k)!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (3*k)! * Stirling1(n,k).
Showing 1-2 of 2 results.

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