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 1-4 of 4 results.

A373619 Expansion of e.g.f. exp(x / (1 - x^2)^(3/2)).

Original entry on oeis.org

1, 1, 1, 10, 37, 316, 2341, 21736, 237385, 2611792, 35911081, 476570656, 7654975021, 121021831360, 2196593121997, 40464132512896, 817485662059921, 17159299818547456, 382733978898335185, 8982388245979044352, 219867829220866999861, 5684505550914409716736
Offset: 0

Views

Author

Seiichi Manyama, Jun 11 2024

Keywords

Crossrefs

Cf. A012150, A088009, A373620.
Cf. A373577.

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n/2-2*k-1,k)/(n-2*k)!.
a(n) == 1 mod 9.
a(n) ~ 3^(1/5) * 5^(-1/2) * exp(3^(-1/5)*n^(1/5)/4 + 5*3^(-3/5)*n^(3/5)/2 - n) * n^(n - 1/5) * (1 - 1/(10*3^(4/5)*n^(1/5))). - Vaclav Kotesovec, Jun 11 2024

A373668 Expansion of e.g.f. exp(x / (1 - x^2)^3).

Original entry on oeis.org

1, 1, 1, 19, 73, 901, 7921, 88831, 1261009, 15786793, 284515201, 4359416491, 88359404761, 1671036171949, 36734936604913, 831051144091351, 19848996799904161, 516144198653004241, 13522792578340917889, 391107276466207593283, 11295497154349628317801
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A012150, A088009, A373619, A373620, A373667.
Cf. A373653, A373682.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, binomial(3*n-5*k-1, k)/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n-5*k-1,k)/(n-2*k)!.
a(n) == 1 (mod 18).

A373681 Expansion of e.g.f. exp(x / (1 - x^2)^2) / (1 - x^2).

Original entry on oeis.org

1, 1, 3, 19, 85, 861, 6391, 74383, 822249, 10724185, 156044971, 2331428331, 40840033213, 706624333429, 14138302767135, 281981427966631, 6273491346471121, 142296558637593393, 3475950835899954259, 88235303457193306435, 2351639524607386287141
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A373682, A373683.
Cf. A373620.

Programs

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

Formula

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

A373667 Expansion of e.g.f. exp(x / (1 - x^2)^(5/2)).

Original entry on oeis.org

1, 1, 1, 16, 61, 676, 5701, 60376, 798841, 9635536, 160878601, 2367914176, 44902245301, 807083463616, 16799688310861, 358223448539776, 8158048770370801, 199405713714155776, 4987832102850957841, 135848995301247809536, 3737769145322321702701
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A012150, A088009, A373619, A373620, A373668.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, binomial(5*n/2-4*k-1, k)/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(5*n/2-4*k-1,k)/(n-2*k)!.
a(n) == 1 (mod 15).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.