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.

A380916 E.g.f. A(x) satisfies A(x) = exp(2 * x / (1 - x*A(x))) / (1 - x*A(x)).

Original entry on oeis.org

1, 3, 20, 254, 4832, 123152, 3947008, 152638320, 6919663360, 359984690432, 21143150157824, 1384004213748224, 99919253031411712, 7887827865170055168, 675952599490594422784, 62495398874421426649088, 6200786173880446466785280, 657212589119205105944428544
Offset: 0

Views

Author

Seiichi Manyama, Feb 08 2025

Keywords

Crossrefs

Programs

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

A380917 E.g.f. A(x) satisfies A(x) = exp(3 * x / (1 - x*A(x))) / (1 - x*A(x)).

Original entry on oeis.org

1, 4, 31, 453, 9957, 293103, 10850625, 484699491, 25381819737, 1525299702363, 103484966417109, 7824985701013143, 652582573442231733, 59509330659228595239, 5890961096785803165129, 629159786981753244521787, 72111288184913038638092337, 8828896697592792281849882547
Offset: 0

Views

Author

Seiichi Manyama, Feb 08 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n, q=3, r=3, s=0, t=1, u=1/3) = 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} 3^k * (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.

A380915 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x)^3)) / (1 - x*A(x)^3).

Original entry on oeis.org

1, 2, 19, 421, 14453, 676741, 40225525, 2901397997, 246222420841, 24038780973913, 2654362957336481, 327087730518759937, 44498835149618922253, 6624743172003104909957, 1071295799491745519081629, 186999332904147675923216341, 35044146207707289182759039825
Offset: 0

Views

Author

Seiichi Manyama, Feb 08 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n, q=1, r=3, 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} (3*n-3*k+1)^(k-1) * binomial(4*n-3*k,n-k)/k!.
Showing 1-3 of 3 results.