A365131 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^3)^2.

1, 2, 11, 62, 395, 2662, 18720, 135738, 1007607, 7619456, 58488028, 454556544, 3569655975, 28282204680, 225796917864, 1814732935968, 14670580718486, 119215212413412, 973246346463636, 7978384233270126, 65649676250344747, 542031604244083664

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A364742, A365132.

Cf. A137952.

Programs

PARI

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