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

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A364987, A364989, A365176, A365177.

Cf. A161633, A213644, A364984.

Sequence in context: A211102 A121973 A223146 * A239765 A006409 A173813

Adjacent sequences: A365172 A365173 A365174 * A365176 A365177 A365178

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved