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 A384089 #11 May 19 2025 09:43:52
%S A384089 1,0,1,63,7206,1357300,384271700,153027592116,81648987014364,
%T A384089 56259916067074896,48646018448463951450,51584263505394472459750,
%U A384089 65833976467770842558152992,99553004175105699906002335098,176031670802373999913671973955080,359870756416991348769957239299854000
%N A384089 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^n.
%F A384089 a(n) = Sum_{0 <= x_1, x_2,..., x_n <= n and x_1 + x_2 + ... + x_n = (n-1)*n} Product_{k=1..n} |Stirling1(n,x_k)|.
%F A384089 a(n) ~ exp(n - 5/3) * n^(2*n+1) / (sqrt(Pi) * n^(3/2) * 2^(n + 1/2)). - _Vaclav Kotesovec_, May 19 2025
%t A384089 Table[SeriesCoefficient[Product[(1 + k*x)^n, {k, 0, n-1}], {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, May 19 2025 *)
%o A384089 (PARI) a(n) = polcoef(prod(k=0, n-1, 1+k*x)^n, n);
%Y A384089 Cf. A342111, A384018, A384029.
%Y A384089 Cf. A351507.
%K A384089 nonn
%O A384089 0,4
%A A384089 _Seiichi Manyama_, May 19 2025