A363357 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))).

1, 1, 7, 85, 1581, 39501, 1244953, 47426373, 2120506489, 108894505753, 6317267871501, 408637512353049, 29164082035045477, 2276557391070945477, 192956160476285907457, 17647873882378895267821, 1732445579330211460781937, 181694902682241512454842673

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

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

Crossrefs

Cf. A362773, A363358.

Cf. A361142.

Sequence in context: A361065 A056547 A293055 * A378410 A121020 A060237

Adjacent sequences: A363354 A363355 A363356 * A363358 A363359 A363360

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved