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.

A373683 Expansion of e.g.f. exp(x / (1 - x^2)) / (1 - x^2).

Original entry on oeis.org

1, 1, 3, 13, 61, 441, 3031, 28813, 267513, 3088081, 36278731, 491262861, 6962025973, 108395586313, 1791145742751, 31601369155021, 594291393830641, 11740929829286433, 246910933786777363, 5406641472165854221, 125497950720670828461, 3018786042678264770521
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A373681, A373682.
Cf. A088009.

Programs

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

Formula

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

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).
Showing 1-3 of 3 results.

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

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