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 A332408 #51 Feb 19 2022 10:22:49
%S A332408 1,1,10,213,8284,513105,46406286,5772636373,945492503320,
%T A332408 197253667623681,51069324556151290,16067283861476491941,
%U A332408 6037615013420387657844,2670812587802323522405393,1373842484756310928089102022,813119045938378747809030359445
%N A332408 a(n) = Sum_{k=0..n} binomial(n,k) * k! * k^n.
%H A332408 Seiichi Manyama, <a href="/A332408/b332408.txt">Table of n, a(n) for n = 0..232</a>
%F A332408 G.f.: Sum_{k>=0} k! * k^k * x^k / (1 - k*x)^(k+1).
%F A332408 a(n) = n! * Sum_{k=0..n} k^n / (n-k)!.
%F A332408 a(n) ~ c * n! * n^n, where c = A073229 = exp(exp(-1)). - _Vaclav Kotesovec_, Feb 20 2021
%F A332408 E.g.f.: Sum_{k>=0} (k*x*exp(x))^k. - _Seiichi Manyama_, Feb 19 2022
%t A332408 Join[{1}, Table[Sum[Binomial[n, k] k! k^n, {k, 0, n}], {n, 1, 15}]]
%o A332408 (PARI) a(n) = sum(k=0, n, binomial(n,k) * k! * k^n); \\ _Michel Marcus_, Apr 24 2020
%o A332408 (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 A332408 Cf. A000522, A006153, A031971, A063170, A072034, A256016, A277452, A332627.
%K A332408 nonn
%O A332408 0,3
%A A332408 _Ilya Gutkovskiy_, Apr 23 2020