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 A355373 #14 Jun 30 2022 08:37:12
%S A355373 1,-1,0,3,40,455,2016,-177373,-11564160,-497664081,-12796467200,
%T A355373 536297904659,132025634657280,14907422733429239,1181852660381503488,
%U A355373 34684559693802943875,-11771644802057621110784,-3553614228958108389522721,-656899368126170250221715456
%N A355373 a(n) = Sum_{k=0..n} k! * (-1)^k * n^(n-k) * Stirling2(n,k).
%F A355373 a(n) = n! * [x^n] n/(n - 1 + exp(n*x)) for n > 0.
%t A355373 a[n_] := Sum[k! * (-1)^k * n^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* _Amiram Eldar_, Jun 30 2022 *)
%o A355373 (PARI) a(n) = sum(k=0, n, k!*(-1)^k*n^(n-k)*stirling(n, k, 2));
%Y A355373 Cf. A212846, A213127, A213128, A213129, A213130, A213131, A213132, A213133.
%Y A355373 Cf. A318183, A352074.
%K A355373 sign
%O A355373 0,4
%A A355373 _Seiichi Manyama_, Jun 30 2022