A381914 Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A002293.

1, 2, 10, 72, 624, 6009, 61809, 664813, 7384613, 84045565, 974913510, 11483316680, 136974177209, 1651166320547, 20083352214058, 246168280262403, 3037682020219285, 37706043912831337, 470482875049515074, 5897864081341146065, 74243055437832292562, 938101296155866961124

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A381915, A381916.

Cf. A381817, A381911.

Cf. A002293.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(2*n-k, n-k)/(n+4*k+1));

Formula

G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x*A(x)).

a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(2*n-k,n-k)/(n+4*k+1).