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 A350722 #16 Feb 04 2022 09:58:39
%S A350722 1,1,33,4567,1652493,1235777551,1656820330173,3619858882041487,
%T A350722 12034209740498292093,57813156798714532953391,
%U A350722 385490564193781368103929213,3454086424032897924417605526607,40500898779980258599522326286912893
%N A350722 a(n) = Sum_{k=0..n} k! * k^(k+n) * Stirling2(n,k).
%F A350722 E.g.f.: Sum_{k>=0} (k * (exp(k*x) - 1))^k.
%F A350722 a(n) ~ exp(exp(-2)/2) * n! * n^(2*n). - _Vaclav Kotesovec_, Feb 04 2022
%t A350722 a[0] = 1; a[n_] := Sum[k! * k^(k+n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 13, 0] (* _Amiram Eldar_, Feb 03 2022 *)
%o A350722 (PARI) a(n) = sum(k=0, n, k!*k^(k+n)*stirling(n, k, 2));
%o A350722 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(k*x)-1))^k)))
%Y A350722 Cf. A122399, A195005, A195263, A338040.
%Y A350722 Cf. A108459, A350721, A351117.
%K A350722 nonn
%O A350722 0,3
%A A350722 _Seiichi Manyama_, Feb 03 2022