A363358 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x)^2)).

1, 1, 7, 91, 1809, 48521, 1643863, 67381875, 3243606817, 179405231761, 11213025902631, 781604862035339, 60120379931640625, 5058593367221610009, 462199816484860893559, 45574025454771003821731, 4823543138131670132557377, 545448517762149418525390625

Offset: 0

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Crossrefs

Cf. A362773, A363357.

Cf. A088695, A363479.

Cf. A361093.

Programs

PARI

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

Formula

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