A377575 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^3.

1, 3, 30, 483, 11100, 334035, 12478698, 558058179, 29104042152, 1735547479587, 116539815603630, 8704631976941043, 716019297815418732, 64326542671867079955, 6267631435921525638738, 658359915933162131600355, 74168964857766293453918928, 8921104769819780822122624323

Offset: 0

Author

Seiichi Manyama, Nov 02 2024

Keywords

• nonn

Crossrefs

Cf. A006153, A377574, A377576.

Cf. A364983, A377554.

Programs

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364983.

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