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.

A371578 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x) )^2.

Original entry on oeis.org

1, 2, 13, 102, 916, 8880, 90607, 958794, 10426089, 115798342, 1308035135, 14980661482, 173553196140, 2030265152576, 23948922940698, 284543368174220, 3402103050539715, 40903437537402792, 494215527894112099, 5997782678374854902, 73078635875447981850
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=2, s=1, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

a(n) = 2 * Sum_{k=0..n} binomial(5*k+2,k) * binomial(k,n-k)/(5*k+2).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365184.

A371585 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x)^2 )^2.

Original entry on oeis.org

1, 2, 15, 130, 1263, 13210, 145254, 1655566, 19385489, 231803136, 2818714210, 34749228048, 433317651224, 5455934825956, 69267925684377, 885756704750960, 11397912218979769, 147483397060856046, 1917785255491649284, 25047838828467708506, 328444729414573179950
Offset: 0

Views

Author

Seiichi Manyama, Mar 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n, r=2, s=2, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Formula

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