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 1-2 of 2 results.

A380769 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x)^2)) / (1 - x*A(x)^2).

Original entry on oeis.org

1, 2, 15, 244, 6097, 206806, 8882599, 462280960, 28279981825, 1989026203114, 158149907916031, 14028441592927180, 1373477000345414353, 147124479131269256254, 17115976784139798114775, 2149092237059821309705816, 289673905062350873773963393, 41719133895880374350508378322
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

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

Formula

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

A380771 E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 + x*A(x)^2)) * (1 + x*A(x)^2).

Original entry on oeis.org

1, 2, 17, 277, 6797, 224301, 9327235, 468615379, 27624235385, 1869871826521, 142960839681311, 12185757382882623, 1145898471300898837, 117849030630765668677, 13159165724143312996907, 1585485015346749680509051, 205026978076680944633853425, 28324382622872897021731667121
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Cf. A380768.

Programs

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

Formula

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