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.

A377890 E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * exp(x * A(x)).

Original entry on oeis.org

1, 2, 15, 211, 4433, 124741, 4412815, 188335981, 9421966209, 540884623753, 35054089163351, 2531882857204273, 201689970517618225, 17567711167993834381, 1661084543502646535967, 169448367505003640681221, 18550123929621138841581185, 2169272360350263071212545553
Offset: 0

Views

Author

Seiichi Manyama, Nov 11 2024

Keywords

Crossrefs

Cf. A088690, A377826, A377891.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(2*n-k+1,n-k)/k!.
E.g.f.: (1/x) * Series_Reversion( x * (exp(-x) - x) ). - Seiichi Manyama, Dec 29 2024

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!.

A379886 E.g.f. A(x) satisfies A(x) = 1/(exp(-x) - x*A(x)^2).

Original entry on oeis.org

1, 2, 15, 247, 6221, 212421, 9181555, 480780875, 29589829785, 2093629793113, 167458531710431, 14942213260220247, 1471585837443194533, 158562898380718019813, 18555214181719160291403, 2343490814996151816116131, 317730224718816177328965425, 46028095309438150072340711601
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A377891, A377893, A379867.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (3*n-3*k+1)^(k-1) * binomial(3*n-3*k+1,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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