A365118 G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^2.

1, 2, 3, 8, 23, 72, 237, 808, 2830, 10118, 36779, 135510, 504935, 1899494, 7204238, 27517766, 105761937, 408715018, 1587169591, 6190357852, 24238696551, 95244997612, 375469654543, 1484519159122, 5885302251250, 23389997790804, 93172394487012

Offset: 0

Author

Seiichi Manyama, Aug 22 2023

Keywords

• nonn

Crossrefs

Cf. A001006, A365119.

Cf. A161634, A378801.

Programs

PARI

a(n, s=1, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = (1 + x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*(n-k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

G.f.: A(x) = (1 + x*B(x))^2 where B(x) is the g.f. of A161634. - Seiichi Manyama, Dec 09 2024