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 A362838 #15 Aug 30 2025 11:48:07
%S A362838 1,0,4,27,704,26250,1573344,137145120,16494166016,2622125642472,
%T A362838 532936224000000,134858889573071400,41584752648545107968,
%U A362838 15351240982641183631440,6684412762278362097401856,3390180844777789569609375000,1981175610959755697378851553280
%N A362838 a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling1(n-k,k)/(n-k)!.
%F A362838 a(n) = n! * [x^n] 1/(1 - n * x)^x.
%F A362838 a(n) ~ sqrt(2*Pi) * n^(2*n - 3/2) / exp(n). - _Vaclav Kotesovec_, Aug 30 2025
%t A362838 Table[n!*SeriesCoefficient[1/(1 - n*x)^x, {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 30 2025 *)
%o A362838 (PARI) a(n) = (-1)^n*n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 1)/(n-k)!);
%Y A362838 Main diagonal of A362837.
%K A362838 nonn,changed
%O A362838 0,3
%A A362838 _Seiichi Manyama_, May 05 2023