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.

A375167 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2)).

Original entry on oeis.org

1, 0, 0, 3, 0, 15, 180, 210, 5040, 51030, 207900, 3991680, 42411600, 356756400, 6485398920, 80635054500, 1040690851200, 19440077857200, 291313362740400, 4914773560897200, 98182334033784000, 1763213788027692000, 35636304386103220800, 778379605589616030000
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^2/2))))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));

Formula

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

A375558 Expansion of e.g.f. 1 / (1 + x * log(1 - x^4/24)).

Original entry on oeis.org

1, 0, 0, 0, 0, 5, 0, 0, 0, 315, 6300, 0, 0, 150150, 6306300, 94594500, 0, 268017750, 17689171500, 549972423000, 7332965640000, 1283268987000, 117632990475000, 5681673439942500, 155840185781280000, 1961530116170625000, 1606200062942475000
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^4/24))))
    
  • PARI
    a(n) = n!*sum(k=0, n\4, (n-4*k)!*abs(stirling(k, n-4*k, 1))/(24^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-4*k)! * |Stirling1(k,n-4*k)|/(24^k*k!).

A375587 Expansion of e.g.f. 1 / (1 + x - x * exp(x^3/6)).

Original entry on oeis.org

1, 0, 0, 0, 4, 0, 0, 70, 1120, 0, 2800, 184800, 2217600, 200200, 39239200, 1513512000, 16166550400, 11435424000, 1029188160000, 31290941281600, 317363510464000, 821292151680000, 52198475641312000, 1387554839326656000, 14092570281613824000, 92349968764253200000
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^3/6))))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/(6^k*k!));

Formula

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