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.

A380830 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x) ).

Original entry on oeis.org

1, 4, 47, 978, 29769, 1201728, 60656679, 3681441648, 261337079601, 21256149703680, 1949700750690879, 199146039242552064, 22420399033075845177, 2758645779752490872832, 368321963942753147683575, 53038788218443786432223232, 8194316429830951008255159009, 1352065789150879084276947222528
Offset: 0

Views

Author

Seiichi Manyama, Feb 05 2025

Keywords

Links

Crossrefs

Cf. A361182, A380826, A380829.
Cf. A088690, A380828.
Cf. A376094.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (3*n+3)^k*binomial(n, k)/(k+1)!);

Formula

E.g.f. A(x) satisfies A(x) = exp(3*x*A(x)) / ( 1 - x*exp(3*x*A(x)) ).
a(n) = n! * Sum_{k=0..n} (3*n+3)^k * binomial(n,k)/(k+1)!.
a(n) = A376094(n+1)/(n+1).

A380808 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x) / (1 + x*exp(-x)) ).

Original entry on oeis.org

1, 3, 24, 335, 6812, 183397, 6168406, 249350285, 11785793352, 638146503593, 38960123581154, 2648475653518081, 198429466488527164, 16246940820392924189, 1443430758561178861758, 138305198841617791230533, 14217431594874334746229520, 1560842183273111251153540945
Offset: 0

Views

Author

Seiichi Manyama, Feb 04 2025

Keywords

Links

Crossrefs

Cf. A088690, A161633, A380826.
Cf. A352448, A380828.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (n+k+2)^k*binomial(n, k)/(k+1)!);

Formula

E.g.f. A(x) satisfies A(x) = exp(2*x*A(x)) / ( 1 - x*exp(x*A(x)) ).
a(n) = n! * Sum_{k=0..n} (n+k+2)^k * binomial(n,k)/(k+1)!.

A380829 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x*exp(-x)) ).

Original entry on oeis.org

1, 4, 45, 891, 25757, 986653, 47235873, 2718521725, 182963698521, 14107443728553, 1226582182222469, 118751669770995913, 12671598073554789909, 1477709279563430592877, 186988047586389278202633, 25518989446806209718773157, 3736444151435292273253963313, 584269287631534621583659461841
Offset: 0

Views

Author

Seiichi Manyama, Feb 05 2025

Keywords

Links

Crossrefs

Cf. A361182, A380826, A380830.

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp(3*x*A(x)) / ( 1 - x*exp(2*x*A(x)) ).
a(n) = n! * Sum_{k=0..n} (2*n+k+3)^k * binomial(n,k)/(k+1)!.
Showing 1-3 of 3 results.

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

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