A365157 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^3 )^2.

1, 2, 15, 124, 1167, 11772, 124561, 1363964, 15326826, 175739698, 2047974619, 24185317182, 288801732423, 3481242975808, 42303574158234, 517683469595912, 6374096109874427, 78909384182870688, 981600144994348111, 12263583888826309544, 153812133876403777005

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A361305, A365158.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(s*k,n-k)/(n+k+1).