A365135 G.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^3)^2.

1, 2, 11, 68, 467, 3418, 26133, 206264, 1667908, 13746476, 115050074, 975180582, 8354044986, 72215867960, 629139381448, 5518236646614, 48689379017014, 431868759238498, 3848616161600778, 34441553184113542, 309390614528633311, 2788841905397090626

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A161797, A365136.

Cf. A006013.

Programs

PARI

a(n, s=3, t=2) = sum(k=0, n, binomial(t*(n+1), k)*binomial(n+(s-1)*k-1, n-k))/(n+1);

Formula

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