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.

A375680 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^2.

Original entry on oeis.org

1, 0, 0, 12, 0, 120, 2160, 3360, 120960, 1632960, 9979200, 255467520, 3592512000, 45664819200, 1070840010240, 18027225216000, 340344048844800, 8174882722406400, 169308486085939200, 4019018956285132800, 104511967278630912000, 2606273308503760896000
Offset: 0

Views

Author

Seiichi Manyama, Aug 23 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375561.
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(k,n-2*k)|/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)!.

A376442 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^3 ).

Original entry on oeis.org

1, 0, 0, 18, 0, 180, 23760, 5040, 1693440, 180260640, 169646400, 42116215680, 4148153856000, 10311946444800, 2266331900152320, 215416210961952000, 1103951255139532800, 227420391096138240000, 21290356810886504140800, 193675502529294757171200, 38377888101603670523904000
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2))^3)/x))
    
  • PARI
    a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*abs(stirling(k, n-2*k, 1))/k!)/(3*n+3)!;

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 + x*A(x) * log(1 - x^2*A(x)^2))^3.
a(n) = (3 * n!/(3n+3)!) * Sum_{k=0..floor(n/2)} (4*n-2*k+2)! * |Stirling1(k,n-2*k)|/k!.
Showing 1-3 of 3 results.