A365134 G.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^2)^3.

1, 3, 18, 130, 1041, 8889, 79310, 730593, 6895575, 66337179, 648087750, 6412437474, 64125877361, 647102364990, 6581050832082, 67384499298690, 694077333315363, 7186898222178342, 74767377019254450, 781105293655408554, 8191332027277068543

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A109081, A365133.

Cf. A365121.

Programs

PARI

a(n, s=2, t=3) = 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).