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 A354752 #13 Jun 07 2022 10:57:17
%S A354752 1,1,0,6,-152,6670,-451152,43685208,-5741360256,984176280288,
%T A354752 -213379094227200,57100689621382176,-18489130293293779968,
%U A354752 7125765731670143814672,-3223822934974620319272960,1692009521117003600170128000,-1019755541584493644326799048704
%N A354752 a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * n^(n-k).
%H A354752 Seiichi Manyama, <a href="/A354752/b354752.txt">Table of n, a(n) for n = 0..233</a>
%F A354752 a(n) = n! * [x^n] 1 / (1 - log(1 + n*x) / n) for n > 0.
%F A354752 a(n) ~ (-1)^(n+1) * n! * n^(n-2). - _Vaclav Kotesovec_, Jun 06 2022
%t A354752 Unprotect[Power]; 0^0 = 1; Table[Sum[StirlingS1[n, k] k! n^(n - k), {k, 0, n}], {n, 0, 16}]
%t A354752 Join[{1}, Table[n! SeriesCoefficient[1/(1 - Log[1 + n x]/n), {x, 0, n}], {n, 1, 16}]]
%o A354752 (PARI) a(n) = sum(k=0, n, stirling(n, k, 1) * k! * n^(n-k)); \\ _Michel Marcus_, Jun 06 2022
%Y A354752 Cf. A006252, A094420, A317171, A317172, A331690, A349731, A352074, A354237, A354750, A354751.
%K A354752 sign
%O A354752 0,4
%A A354752 _Ilya Gutkovskiy_, Jun 06 2022