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 A321989 #13 Dec 19 2018 17:52:44
%S A321989 1,0,1,2,12,64,455,3618,33131,338728,3838572,47678520,644172045,
%T A321989 9402091620,147405489205,2470129035710,44053120590540,833000495161600,
%U A321989 16644648834503555,350406040769989974,7751328201878523295,179738821179613739780,4359334293132050359932,110368937036048741434824
%N A321989 Expansion of e.g.f. exp(exp(-x)/(1 - x) - 1).
%F A321989 a(0) = 1; a(n) = Sum_{k=1..n} A000166(k)*binomial(n-1,k-1)*a(n-k).
%F A321989 a(n) ~ exp(3*exp(-1)/2 - 5/4 + 2*exp(-1/2)*sqrt(n) - n) * n^(n-1/4) / sqrt(2). - _Vaclav Kotesovec_, Dec 19 2018
%p A321989 seq(coeff(series(factorial(n)*exp(exp(-x)/(1-x)-1),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Dec 19 2018
%t A321989 nmax = 23; CoefficientList[Series[Exp[Exp[-x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A321989 a[n_] := a[n] = Sum[Subfactorial[k] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
%Y A321989 Cf. A000166, A000262, A318365, A321974.
%K A321989 nonn
%O A321989 0,4
%A A321989 _Ilya Gutkovskiy_, Dec 19 2018