This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374844 #16 Feb 16 2025 08:34:07
%S A374844 0,1,6,45,436,5305,78486,1372945,27760776,637267473,16372674730,
%T A374844 465411092641,14501033559948,491388542871577,17991446425760094,
%U A374844 707765586767260785,29770993461985724176,1333347150740094075169,63346656788618230928466
%N A374844 a(n) = n! * Sum_{k=1..n} k^k / k!.
%H A374844 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A374844 a(0) = 0; a(n) = n*a(n-1) + n^n.
%F A374844 a(n) = A277506(n) - n!.
%F A374844 E.g.f.: -1/( (1 + 1/LambertW(-x)) * (1 - x) ).
%F A374844 a(n) ~ n^n / (1 - exp(-1)). - _Vaclav Kotesovec_, Jul 22 2024
%p A374844 a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 0:
%p A374844 seq(a(n), n=0..23); # _Alois P. Heinz_, Jul 22 2024
%o A374844 (PARI) a(n) = n!*sum(k=1, n, k^k/k!);
%Y A374844 Cf. A007526, A030297, A337001, A337002.
%Y A374844 Cf. A000142, A277506.
%K A374844 nonn
%O A374844 0,3
%A A374844 _Seiichi Manyama_, Jul 22 2024