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 1-2 of 2 results.

A375679 Expansion of e.g.f. 1 / (1 + x^2 * log(1 - x))^3.

Original entry on oeis.org

1, 0, 0, 18, 36, 120, 4860, 33264, 241920, 5598720, 72364320, 879500160, 18172978560, 331463508480, 5726430597888, 126134466796800, 2836325702246400, 62773403361177600, 1562890149787392000, 41009994647421972480, 1090182759179092992000
Offset: 0

Views

Author

Seiichi Manyama, Aug 23 2024

Keywords

Crossrefs

Cf. A351503, A375639.
Cf. A375663.

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A351503.
a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (k+2)! * |Stirling1(n-2*k,k)|/(n-2*k)!.

A376436 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x))^2 ).

Original entry on oeis.org

1, 0, 0, 12, 24, 80, 11160, 87696, 715680, 62337600, 1065980160, 15842534400, 1109943362880, 31591940440320, 731706348941568, 46767587926752000, 1889337264901632000, 61735665488234250240, 3896148715287564902400, 201584132714100384460800, 8661099107269708639948800, 567405718655558932535500800
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2024

Keywords

Links

Crossrefs

Cf. A376385, A376392.
Cf. A371235, A375639.

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 + x^2*A(x)^2 * log(1 - x*A(x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371235.
a(n) = (2 * n!/(2*n+2)!) * Sum_{k=0..floor(n/3)} (2*n+k+1)! * |Stirling1(n-2*k,k)|/(n-2*k)!.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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