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 1-4 of 4 results.

A357966 Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).

Original entry on oeis.org

1, 0, 0, 6, 0, 60, 360, 840, 20160, 75600, 1058400, 10311840, 79833600, 1305944640, 11018367360, 174616041600, 2150397849600, 28661419987200, 473667677683200, 6293779652160000, 114484773731328000, 1766543101087564800, 31640707215390873600
Offset: 0

Views

Author

Seiichi Manyama, Oct 22 2022

Keywords

Crossrefs

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(k,n-2*k)/k!.

A357968 Expansion of e.g.f. exp( x * (exp(x^4) - 1) ).

Original entry on oeis.org

1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 1814400, 0, 0, 1037836800, 43589145600, 217945728000, 0, 14820309504000, 1867358997504000, 30411275102208000, 101370917007360000, 425757851430912000, 140500090972200960000, 5385836820601036800000
Offset: 0

Views

Author

Seiichi Manyama, Oct 22 2022

Keywords

Crossrefs

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} Stirling2(k,n-4*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!.

A375592 Expansion of e.g.f. exp( x * (exp(x^3/6) - 1) ).

Original entry on oeis.org

1, 0, 0, 0, 4, 0, 0, 70, 560, 0, 2800, 92400, 369600, 200200, 19619600, 252252000, 695094400, 5717712000, 171531360000, 1307259553600, 4852431584000, 136882025280000, 2175699958432000, 12698089211808000, 150837908212992000, 3848134863773200000
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)-1))))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, stirling(k, n-3*k, 2)/(6^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(k,n-3*k)/(6^k*k!).
Showing 1-4 of 4 results.