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.

A376346 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^3)) ).

Original entry on oeis.org

1, 0, 0, 0, 24, 0, 0, 2520, 201600, 0, 1209600, 259459200, 16765056000, 1556755200, 639307468800, 100037089152000, 5967179676057600, 2815858805760000, 784290778951680000, 107737010595422208000, 6175610876944244736000, 8813187524619878400000, 2070195245189633802240000, 264886226510800191897600000
Offset: 0

Views

Author

Seiichi Manyama, Sep 21 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (2*n-3*k)! * |Stirling1(k,n-3*k)|/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!.

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.