A371583 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x) )^2.

1, 2, 13, 104, 940, 9166, 94044, 1000602, 10939780, 122161128, 1387361151, 15974899766, 186069556707, 2188416960148, 25953579753464, 310022550197360, 3726709235290628, 45047517497268968, 547217895030263028, 6676784544374859088, 81789906534091716353

Offset: 0

Author

Seiichi Manyama, Mar 28 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..896

Crossrefs

Cf. A045868, A270386, A371518, A371523.

Cf. A349332, A371486, A371520.

Cf. A371578, A371585.

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(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-1,n-k)/(5*k+2).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349332.