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.

A371147 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^(x^2*A(x)^2).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 2700, 21168, 173040, 7611840, 125415360, 1848591360, 71211998880, 1844075600640, 41500836336960, 1609925690419200, 55708371912211200, 1719475797882286080, 72091120665964654080, 3046645011228998860800, 119757727692451283097600
Offset: 0

Views

Author

Seiichi Manyama, Mar 13 2024

Keywords

Links

Crossrefs

Cf. A184949, A371145.

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.
E.g.f.: (1/x) * Series_Reversion( x*(1 - x)^(x^2) ). - Seiichi Manyama, Sep 21 2024

A376351 E.g.f. satisfies A(x) = exp( x*A(x)*(exp(x^2*A(x)^2) - 1) ).

Original entry on oeis.org

1, 0, 0, 6, 0, 60, 2520, 840, 181440, 6063120, 11642400, 1437337440, 44626982400, 254278664640, 24575197046400, 756010400745600, 9284429893939200, 784770965801222400, 25067890370095372800, 541810656586725926400, 42351473267452597248000, 1461224653966598493772800, 48020130717168717960652800
Offset: 0

Views

Author

Seiichi Manyama, Sep 21 2024

Keywords

Links

Crossrefs

Cf. A030019, A356785, A371145.
Cf. A357966.

Programs

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

Formula

E.g.f.: (1/x) * Series_Reversion( x*exp(x*(1 - exp(x^2))) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * Stirling2(k,n-2*k)/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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