A365175 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)).

1, 1, 10, 189, 5476, 215145, 10701006, 644909503, 45687408712, 3721382812305, 342689189598010, 35206864089944151, 3992473080042706524, 495361299387667990537, 66752437447119717428422, 9708649781691227748131535, 1515863453268825963300368656

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A364987, A364989, A365176, A365177.

Cf. A161633, A213644, A364984.

Programs

PARI

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

Formula

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