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.

A379867 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^2) - x*A(x)^2).

Original entry on oeis.org

1, 2, 23, 529, 18589, 884281, 53195407, 3874595089, 331580316473, 32614443047521, 3625839880813171, 449629404853604185, 61535275741655857621, 9213155228282408405185, 1498018121369750569371959, 262869047482982449625840161, 49515850496472530668242845041
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2025

Keywords

Crossrefs

Cf. A377890, A379870.
Cf. A377892, A379884.
Cf. A377891, A377893, A379886.
Cf. A364985, A379864.

Programs

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

Formula

E.g.f.: sqrt( (1/x) * Series_Reversion( x * (exp(-x) - x)^2 ) ).
a(n) = n! * Sum_{k=0..n} (3*n-k+1)^(k-1) * binomial(3*n-k+1,n-k)/k!.

A379934 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)) - x )^2.

Original entry on oeis.org

1, 4, 38, 626, 15008, 476122, 18864124, 898099526, 49988162672, 3187006372466, 229091274174404, 18335328399262030, 1617287276785929928, 155893591123924724618, 16304903025947743812476, 1839154613521698544945238, 222562344165125395485931232, 28763041177430039602579211746
Offset: 0

Views

Author

Seiichi Manyama, Jan 06 2025

Keywords

Crossrefs

Cf. A379933, A379936.
Cf. A379864, A379884.

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379884.
a(n) = 2 * n! * Sum_{k=0..n} (n+k+2)^(k-1) * binomial(n+k+2,n-k)/k!.

A379935 E.g.f. A(x) satisfies A(x) = 1/( exp(-x) - x*A(x) )^2.

Original entry on oeis.org

1, 4, 38, 674, 17744, 623362, 27480844, 1460031610, 90862627184, 6485745312098, 522469881832964, 46895105170999978, 4641403797239576392, 502226056825606487506, 58985555898802967473820, 7473459685930447455067418, 1016083115772085962460442336, 147559760656716707828287356610
Offset: 0

Views

Author

Seiichi Manyama, Jan 06 2025

Keywords

Crossrefs

Cf. A379864, A379886, A379933.

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379886.
a(n) = 2 * n! * Sum_{k=0..n} (3*n-3*k+2)^(k-1) * binomial(3*n-3*k+2,n-k)/k!.
Showing 1-3 of 3 results.

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

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