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.

A371302 E.g.f. satisfies A(x) = 1/(1 + x^2*log(1 - x*A(x))).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 1620, 13608, 117600, 2924640, 49603680, 782147520, 19083936960, 463369645440, 10836652514688, 304533583200000, 9218842256332800, 281872333420554240, 9421579421176089600, 338543319734116116480, 12590519274541116518400
Offset: 0

Views

Author

Seiichi Manyama, Mar 18 2024

Keywords

Crossrefs

Cf. A370994, A371118, A371138.
Cf. A351503.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\3, (n-k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-2*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k)! * |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-2*k+1)! ).

A376292 E.g.f. satisfies A(x) = 1 - (x*A(x))^3 * log(1 - x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 24, 60, 240, 1260, 169344, 1693440, 17150400, 187941600, 12778698240, 271809457920, 5031211086720, 91848556800000, 4643532967772160, 154079136039628800, 4367731446302515200, 117143657916761548800, 5457792037686441984000
Offset: 0

Views

Author

Seiichi Manyama, Sep 19 2024

Keywords

Links

Crossrefs

Cf. A138013, A371121, A371138.

Programs

  • PARI
    a(n) = n!^2*sum(k=0, n\4, abs(stirling(n-3*k, k, 1))/((n-3*k)!*(n-k+1)!));

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/4)} |Stirling1(n-3*k,k)|/( (n-3*k)! * (n-k+1)! ).
E.g.f.: (1/x) * Series_Reversion( x/(1 - x^3*log(1 - x)) ).
Showing 1-2 of 2 results.

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