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.

A375799 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2).

Original entry on oeis.org

1, 1, 2, 6, 36, 240, 1800, 16800, 178080, 2086560, 27518400, 399168000, 6286896000, 107623676160, 1984274772480, 39143052748800, 824445099878400, 18450791322163200, 437015358530150400, 10929450232744243200, 287728555881102336000, 7952251084537503744000
Offset: 0

Views

Author

Seiichi Manyama, Aug 29 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.

A375806 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^2.

Original entry on oeis.org

1, 2, 6, 30, 192, 1520, 14220, 153720, 1881600, 25728192, 388402560, 6415960320, 115078138560, 2227056923520, 46247253212160, 1025696098627200, 24195406204569600, 604862279807385600, 15973029429800002560, 444299711254300661760, 12983645995613669376000
Offset: 0

Views

Author

Seiichi Manyama, Aug 29 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)^2))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375798.
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(n-k,n-2*k)|/(n-k)!.

A375807 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^3.

Original entry on oeis.org

1, 3, 12, 69, 504, 4440, 45720, 538020, 7116480, 104455008, 1684005120, 29571696000, 561695238720, 11472451848000, 250694772007680, 5835284153899200, 144124039400140800, 3764378233282867200, 103661897106414366720, 3001493647870874956800
Offset: 0

Views

Author

Seiichi Manyama, Aug 29 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)^3))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375798.
a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * |Stirling1(n-k,n-2*k)|/(n-k)!.
Showing 1-3 of 3 results.