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 A277506 #10 May 12 2021 22:36:42
%S A277506 1,2,8,51,460,5425,79206,1377985,27801096,637630353,16376303530,
%T A277506 465451009441,14501512561548,491394769892377,17991533604051294,
%U A277506 707766894441628785,29771014384775612176,1333347506427522171169,63346663190991936656466,3182006256289160385596833
%N A277506 E.g.f.: 1/((1+LambertW(-x))*(1-x)).
%H A277506 G. C. Greubel, <a href="/A277506/b277506.txt">Table of n, a(n) for n = 0..385</a>
%F A277506 For n > 0, a(n) = n! + Sum_{k=1..n} binomial(n,k) * k^k * (n-k)!.
%F A277506 a(n) ~ n^n / (1-exp(-1)).
%F A277506 a(n) = n*a(n-1) + n^n, a(0) = 1. - _Alois P. Heinz_, May 12 2021
%p A277506 a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 1:
%p A277506 seq(a(n), n=0..23); # _Alois P. Heinz_, May 12 2021
%t A277506 CoefficientList[Series[1/(1+LambertW[-x])/(1-x), {x, 0, 20}], x] * Range[0, 20]!
%t A277506 Flatten[{1, Table[n! + Sum[Binomial[n, k]*k^k*(n-k)!, {k, 1, n}], {n, 1, 20}]}]
%o A277506 (PARI) x='x+O('x^50); Vec(serlaplace(1/((1 + lambertw(-x))*(1-x)))) \\ _G. C. Greubel_, Nov 12 2017
%Y A277506 Cf. A277507.
%K A277506 nonn
%O A277506 0,2
%A A277506 _Vaclav Kotesovec_, Oct 18 2016