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 A318615 #9 Aug 31 2018 03:08:39
%S A318615 1,0,4,9,224,1650,38664,540960,13930496,291769128,8598924000,
%T A318615 237964577400,8082061452288,275311724996880,10714824398213376,
%U A318615 430458433091505000,19007133744632954880,876046954673290438080,43416883192646088235008,2252711496770428822876800,124040138653975179571200000
%N A318615 a(n) = n! * [x^n] 1/(1 - x)^(n*x).
%H A318615 Vaclav Kotesovec, <a href="/A318615/b318615.txt">Table of n, a(n) for n = 0..380</a>
%F A318615 a(n) = n! * [x^n] exp(n*x*Sum_{k>=1} x^k/k).
%F A318615 a(n) = (-1)^n*n! * Sum_{k=0..n} n^(n-k)*Stirling1(k,n-k)/k!.
%F A318615 a(n) ~ n^n / (sqrt(1 - (1-s)*(2-s)*s) * exp(n) * s^n * (1-s)^(s*n - 1)), where s = 0.530402312512063468084914246777198746... is the root of the equation (1-s)*(2 + s + s*log(1-s)) = 1. - _Vaclav Kotesovec_, Aug 30 2018
%t A318615 Table[n! SeriesCoefficient[1/(1 - x)^(n x), {x, 0, n}], {n, 0, 20}]
%t A318615 Join[{1}, Table[(-1)^n n! Sum[n^(n - k) StirlingS1[k, n - k]/k!, {k, n}], {n, 20}]]
%Y A318615 Cf. A007113, A008275, A053489, A053490, A191415, A318616.
%K A318615 nonn
%O A318615 0,3
%A A318615 _Ilya Gutkovskiy_, Aug 30 2018