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 A332627 #45 Feb 19 2022 10:22:59
%S A332627 1,1,6,117,4388,266065,23731314,2923345621,475364541672,
%T A332627 98623225721601,25421365316232710,7969388199705535141,
%U A332627 2985785305877403047820,1317500933136749853197329,676266417871227455138941242,399516621958550611386236160405
%N A332627 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * k! * k^n.
%H A332627 Seiichi Manyama, <a href="/A332627/b332627.txt">Table of n, a(n) for n = 0..232</a>
%F A332627 G.f.: Sum_{k>=0} k! * k^k * x^k / (1 + k*x)^(k+1).
%F A332627 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^n / (n-k)!.
%F A332627 a(n) ~ c * n! * n^n, where c = A072364 = exp(-exp(-1)). - _Vaclav Kotesovec_, Jul 10 2021
%F A332627 E.g.f.: Sum_{k>=0} (k*x*exp(-x))^k. - _Seiichi Manyama_, Feb 19 2022
%t A332627 Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] k! k^n, {k, 0, n}], {n, 1, 15}]]
%o A332627 (PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n,k) * k! * k^n); \\ _Michel Marcus_, Apr 24 2020
%o A332627 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x*exp(-x))^k))) \\ _Seiichi Manyama_, Feb 19 2022
%Y A332627 Cf. A000166, A120485, A134095, A302397, A319392, A332408.
%K A332627 nonn
%O A332627 0,3
%A A332627 _Ilya Gutkovskiy_, Apr 23 2020