A374844 - OEIS

%I #15 Jul 22 2024 11:48:37

%S 0,1,6,45,436,5305,78486,1372945,27760776,637267473,16372674730,

%T 465411092641,14501033559948,491388542871577,17991446425760094,

%U 707765586767260785,29770993461985724176,1333347150740094075169,63346656788618230928466

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

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

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

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

%F a(n) ~ n^n / (1 - exp(-1)). - _Vaclav Kotesovec_, Jul 22 2024

%p a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 0:

%p seq(a(n), n=0..23);  # _Alois P. Heinz_, Jul 22 2024

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

%Y Cf. A007526, A030297, A337001, A337002.

%Y Cf. A000142, A277506.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 22 2024