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.

A375681 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^3.

Original entry on oeis.org

1, 0, 0, 18, 0, 180, 4320, 5040, 241920, 3900960, 19958400, 622702080, 9580032000, 112086374400, 3013462932480, 52540488000000, 977094287769600, 25683596370432000, 540291743902310400, 13061642656398336000, 360218657273739264000, 9111103133582241792000
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))^3))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(k, n-2*k, 1))/k!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375561.
a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * |Stirling1(k,n-2*k)|/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)!.

A376441 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^2 ).

Original entry on oeis.org

1, 0, 0, 12, 0, 120, 10800, 3360, 766080, 56064960, 76507200, 12988926720, 885913459200, 3162288729600, 477701680135680, 31728803730624000, 230820218044416000, 32828647402065715200, 2173902177236319129600, 27658882036996206796800, 3801535675181689116672000, 255228267875636473786368000
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))^2)/x))
    
  • PARI
    a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!)/(2*n+2)!;

Formula

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