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.

A375795 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x).

Original entry on oeis.org

1, 1, 2, 9, 48, 320, 2580, 24150, 258720, 3117744, 41741280, 614774160, 9877412160, 171923225760, 3222634615200, 64721762305200, 1386495651340800, 31558444491974400, 760564843136017920, 19348085890139086080, 518103061345155686400, 14567452481227893811200
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-(exp(x^2)-1)/x)))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(n-k, n-2*k, 2)/(n-k)!);

Formula

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

A375813 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^3.

Original entry on oeis.org

1, 3, 12, 60, 396, 3240, 30960, 335160, 4072320, 54976320, 815119200, 13152585600, 229441766400, 4303027048320, 86318858545920, 1843929831744000, 41786821607731200, 1001231951502182400, 25288602517469491200, 671488122628741017600
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-(exp(x^3)-1)/x^2)^3))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k+2)!*stirling(n-2*k, n-3*k, 2)/(n-2*k)!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375796.
a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (n-3*k+2)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.

A375812 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^2.

Original entry on oeis.org

1, 2, 6, 24, 144, 1080, 9360, 92400, 1038240, 13063680, 181137600, 2744280000, 45145900800, 801313793280, 15256927445760, 310158565516800, 6705376386508800, 153609543947059200, 3716764672074854400, 94715288771578675200, 2535525218048030208000
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-(exp(x^3)-1)/x^2)^2))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k+1)!*stirling(n-2*k, n-3*k, 2)/(n-2*k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375796.
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.
Showing 1-3 of 3 results.