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 A317366 #7 Jul 26 2018 16:27:46
%S A317366 1,2,8,47,359,3347,36665,460098,6494444,101708007,1748263435,
%T A317366 32697711895,660642793717,14332871438810,332186039584768,
%U A317366 8188070581358795,213821204277955267,5895325327054011087,171095582314380667621,5212792218964517899506,166321395872186089502972,5545223090189205308551443
%N A317366 Expansion of e.g.f. exp(exp(x/(1 - x)) - 1)/(1 - x).
%F A317366 a(n) = Sum_{k=0..n} binomial(n,k)^2*k!*Bell(n-k), where Bell() = A000110.
%p A317366 a:= proc(n) option remember; add(binomial(n, k)^2
%p A317366 *k!*combinat[bell](n-k), k=0..n)
%p A317366 end:
%p A317366 seq(a(n), n=0..30); # _Alois P. Heinz_, Jul 26 2018
%t A317366 nmax = 21; CoefficientList[Series[Exp[Exp[x/(1 - x)] - 1]/(1 - x) , {x, 0, nmax}], x] Range[0, nmax]!
%t A317366 Table[Sum[Binomial[n, k]^2 k! BellB[n - k], {k, 0, n}], {n, 0, 21}]
%Y A317366 Cf. A000110, A002720, A084357, A101053.
%K A317366 nonn
%O A317366 0,2
%A A317366 _Ilya Gutkovskiy_, Jul 26 2018