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.

A377742 E.g.f. satisfies A(x) = exp(x) / (1 - x * A(x))^2.

Original entry on oeis.org

1, 3, 23, 331, 7133, 205901, 7470475, 326932299, 16768124217, 986753701657, 65548017270791, 4852285640543639, 396133183892522389, 35359325061987638661, 3426053898460864501251, 358128187005971803014211, 40172982580368589391407217, 4813677071886578522596221233
Offset: 0

Views

Author

Seiichi Manyama, Nov 05 2024

Keywords

Crossrefs

Programs

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

Formula

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

A380752 E.g.f. A(x) satisfies A(x) = exp(x * A(x)) / (1 - x * A(x)^2)^2.

Original entry on oeis.org

1, 3, 41, 1114, 46217, 2595186, 184264033, 15839938318, 1599772132337, 185698542344050, 24362771800087241, 3565209717372983142, 575786158331135496313, 101729690893078619387914, 19518889966696995273600209, 4041785999884112498658681406, 898403694387449768732923267937
Offset: 0

Views

Author

Seiichi Manyama, Feb 01 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380753 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x * A(x)^2)^2.

Original entry on oeis.org

1, 3, 47, 1453, 68349, 4344751, 348936139, 33912469305, 3871084443641, 507765120717691, 75265926888996711, 12443096536067016997, 2270083842550815380725, 453042725968243823206887, 98183026886745981671902979, 22962952582930039784948279281, 5764815614414943166224203759601
Offset: 0

Views

Author

Seiichi Manyama, Feb 01 2025

Keywords

Crossrefs

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(5*n-k+1,n-k)/k!.
Showing 1-3 of 3 results.