A365058 E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x/2 * A(x)^3)).

1, 1, 8, 130, 3250, 110336, 4744984, 247321096, 15155937500, 1067967873280, 85084447796416, 7562971176299936, 742055168686622872, 79662784245760000000, 9288538211005096189280, 1168938868353871429273216, 157924822350438542185141264

Offset: 0

Author

Seiichi Manyama, Aug 19 2023

Keywords

• nonn

Crossrefs

Cf. A091485, A365057.

Cf. A363479.

Programs

PARI

a(n) = n!*sum(k=0, n, (1/2)^(n-k)*(3*n+1)^(k-1)*binomial(k, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (3*n+1)^(k-1) * binomial(k,n-k)/k!.