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 A158094 #17 Jun 18 2019 06:51:59
%S A158094 1,2,4,20,92,580,4156,34372,314348,3204116,35703996,433587396,
%T A158094 5687955724,80265513140,1211781628060,19497537309028,333041104402860,
%U A158094 6019819589363348,114794574818830716,2303337794614783236
%N A158094 G.f. Product_{n>=1} (1 + a(n)*x^n) = Sum_{n>=0} n!*x^n.
%H A158094 Robert Israel, <a href="/A158094/b158094.txt">Table of n, a(n) for n = 1..450</a>
%F A158094 a(n) ~ n! * (1 - 1/n - 1/n^2 - 4/n^3 - 23/n^4 - 171/n^5 - 1542/n^6 - 16241/n^7 - 194973/n^8 - 2622610/n^9 - 39027573/n^10 - ...), for coefficients see A113869. - _Vaclav Kotesovec_, Jun 18 2019
%p A158094 A158094:= proc(n)
%p A158094 option remember;
%p A158094 local S;
%p A158094 S:= series(add(k!*x^k,k=0..n)/mul(1+A158094(k)*x^k,k=1..n-1),x,n+1);
%p A158094 coeff(S,x,n)
%p A158094 end; # _Robert Israel_, Mar 04 2014
%t A158094 a[n_] := a[n] = Module[{s}, s = Series[Sum[k!*x^k, {k, 0, n}]/Product[1+a[k]*x^k, {k, 1, n-1}], {x, 0, n+1}]; Coefficient[s, x, n]]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Mar 04 2014, after Maple *)
%o A158094 (PARI) {a(n)=if(n<1, 0, polcoeff(sum(k=0,n,k!*x^k)/prod(k=1, n-1, 1+a(k)*x^k +x*O(x^n)), n))}
%Y A158094 Cf. A316084.
%K A158094 nonn
%O A158094 1,2
%A A158094 _Paul D. Hanna_, Apr 15 2009