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.

A373682 Expansion of e.g.f. exp(x / (1 - x^2)^3) / (1 - x^2).

Original entry on oeis.org

1, 1, 3, 25, 109, 1401, 11191, 147673, 1887705, 26419249, 454408651, 7265533881, 148341346693, 2804459457385, 63733061703039, 1419987630142201, 35144931608633521, 902380834051682913, 24277141650582775315, 699721521711883149529, 20520810981571082937501
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A373681, A373683.
Cf. A373668.

Programs

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

Formula

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

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).

A373684 Expansion of e.g.f. exp(x / (1 - x^3)) / (1 - x^3).

Original entry on oeis.org

1, 1, 1, 7, 49, 181, 1201, 16171, 122977, 971209, 16788961, 206578351, 2094314641, 40260673597, 694617709969, 9088535091091, 187060085419201, 4109646055718161, 68029103349383617, 1498126927153125079, 39199612737165358321, 799248202624341298501
Offset: 0

Views

Author

Seiichi Manyama, Jun 13 2024

Keywords

Crossrefs

Cf. A002720, A373683.
Cf. A293493.

Programs

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k,k)/(n-3*k)!.
a(n) == 1 (mod 6).
Showing 1-3 of 3 results.

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

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