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.

A375561 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2)).

Original entry on oeis.org

1, 0, 0, 6, 0, 60, 720, 1680, 40320, 453600, 3326400, 67858560, 878169600, 11935123200, 240708948480, 3946374432000, 73927190937600, 1621341859737600, 32960791774310400, 758085507686707200, 18570669277095936000, 454016684061997056000, 12100759898595611443200
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

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

Formula

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

A375589 Expansion of e.g.f. 1 / (1 + x - x * exp(x^3)).

Original entry on oeis.org

1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 604800, 39916800, 479001600, 259459200, 50854003200, 1961511552000, 21097146470400, 88921857024000, 8002967132160000, 243459152346009600, 2642401903325184000, 38318206628782080000, 2435557926202232832000
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * Stirling2(k,n-3*k)/k!.

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!.
Showing 1-3 of 3 results.