A380514 Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.

1, 1, 5, 67, 1537, 50021, 2107021, 108885295, 6665443457, 471522589417, 37843890892021, 3397250515809371, 337267132243022785, 36687625652474612557, 4339368321317331858557, 554467482301151809302151, 76112537023512618262963201, 11170667360636927554290623825, 1745500813880455301486766050917

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

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

Crossrefs

Cf. A002293, A069271, A380513, A380515, A380516.

Sequence in context: A123034 A382058 A166619 * A323208 A262656 A383561

Adjacent sequences: A380511 A380512 A380513 * A380515 A380516 A380517

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2025

Status

approved