A365130 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^2)^3.

1, 3, 18, 124, 945, 7650, 64592, 562419, 5013645, 45530725, 419735784, 3917714430, 36949853641, 351597275136, 3371317098546, 32542166997655, 315962469096855, 3083729075615055, 30236064140642514, 297698542934231016, 2942082095638037148

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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).

Prog

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

Crossrefs

Cf. A161634, A365129.

Cf. A137953.

Sequence in context: A305869 A371483 A181998 * A349024 A176277 A289429

Adjacent sequences: A365127 A365128 A365129 * A365131 A365132 A365133

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved