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.

A364742 G.f. satisfies A(x) = 1 / (1 - x*(1 + x*A(x))^3).

Original entry on oeis.org

1, 1, 4, 13, 50, 201, 841, 3627, 15993, 71803, 327082, 1508002, 7023446, 32995626, 156173668, 744029238, 3565030063, 17169013899, 83061503584, 403483653745, 1967217524551, 9623463731721, 47220968518786, 232354408276613, 1146254897566224, 5668118931395946
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Programs

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

Formula

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

A364743 G.f. satisfies A(x) = 1 / (1 - x*(1 + x*A(x))^4).

Original entry on oeis.org

1, 1, 5, 19, 85, 402, 1971, 9976, 51633, 272131, 1455486, 7879664, 43096967, 237777710, 1321792096, 7396125088, 41624735353, 235461758085, 1338049873395, 7634930866465, 43726638130854, 251273386911443, 1448362622788376, 8371936106228253
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*k, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(4*k,n-k).

A364763 G.f. satisfies A(x) = 1 / (1 + x*(1 + x*A(x))^5).

Original entry on oeis.org

1, -1, -4, 4, 51, -6, -770, -694, 12363, 25583, -198824, -701944, 3049603, 17238467, -41348631, -396817391, 391720363, 8689985437, 1902247845, -181526287908, -253530149234, 3597968506523, 9727546141524, -66671292054788, -291760189535999, 1116731578365699
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Programs

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

Formula

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