A374844 a(n) = n! * Sum_{k=1..n} k^k / k!.

0, 1, 6, 45, 436, 5305, 78486, 1372945, 27760776, 637267473, 16372674730, 465411092641, 14501033559948, 491388542871577, 17991446425760094, 707765586767260785, 29770993461985724176, 1333347150740094075169, 63346656788618230928466

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

a(0) = 0; a(n) = n*a(n-1) + n^n.

a(n) = A277506(n) - n!.

E.g.f.: -1/( (1 + 1/LambertW(-x)) * (1 - x) ).

a(n) ~ n^n / (1 - exp(-1)). - Vaclav Kotesovec, Jul 22 2024

Maple

a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 0:
seq(a(n), n=0..23);  # Alois P. Heinz, Jul 22 2024

Prog

(PARI) a(n) = n!*sum(k=1, n, k^k/k!);

Crossrefs

Cf. A007526, A030297, A337001, A337002.

Cf. A000142, A277506.

Sequence in context: A019577 A097814 A239910 * A228194 A331726 A084064

Adjacent sequences: A374841 A374842 A374843 * A374845 A374846 A374847

Keyword

nonn

Author

Seiichi Manyama, Jul 22 2024

Status

approved