A380603 Expansion of e.g.f. exp(2*x*G(x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

1, 2, 12, 140, 2512, 61392, 1905184, 71781824, 3183563520, 162497556224, 9383803201024, 604888546242048, 43056560538093568, 3354362248463544320, 283895464602180231168, 25938521255822517813248, 2544584391277895815069696, 266765818037212169468706816, 29764238411096397030375424000

Offset: 0

Author

Seiichi Manyama, Jan 28 2025

Keywords

• nonn

Crossrefs

Cf. A001764, A251573, A380511.

Programs

PARI

a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, 2^(n-k)*binomial(2*n+k, k)/((2*n+k)*(n-k-1)!)));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380511.

a(n) = 2 * n! * Sum_{k=0..n-1} 2^(n-k) * binomial(2*n+k,k)/((2*n+k) * (n-k-1)!) for n > 0.