A377576 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^4.

1, 4, 52, 1116, 34408, 1394340, 70298424, 4248802516, 299752943200, 24196951718532, 2200519882434280, 222683725755611604, 24824104612186789584, 3023063956714780554628, 399343825987950226379416, 56879649386095684434783060, 8689968793295620150120679104

Offset: 0

Author

Seiichi Manyama, Nov 02 2024

Keywords

• nonn

Crossrefs

Cf. A006153, A377574, A377575.

Cf. A364987, A377577.

Programs

PARI

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

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A364987.

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