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 A328008 #9 Oct 02 2019 06:21:35
%S A328008 1,2,13,124,1575,25006,476421,10589720,269010979,7687905826,
%T A328008 244120131393,8526912775756,324914136199263,13412430958497494,
%U A328008 596253684006657085,28399969571266895488,1442890578572155475355,77889310498718258171914,4451905168738601015593785
%N A328008 Expansion of e.g.f. 1 / (2 - exp(x) / (1 - x)).
%F A328008 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000522(k) * a(n-k).
%F A328008 a(n) ~ n! / (2*(1 + 1/LambertW(exp(1)/2)) * (1 - LambertW(exp(1)/2))^(n+1)). - _Vaclav Kotesovec_, Oct 02 2019
%t A328008 nmax = 18; CoefficientList[Series[1/(2 - Exp[x]/(1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
%t A328008 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Floor[Exp[1] k!] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%o A328008 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(2-exp(x)/(1-x)))) \\ _Michel Marcus_, Oct 02 2019
%Y A328008 Cf. A000522, A002866, A321974, A328007.
%K A328008 nonn
%O A328008 0,2
%A A328008 _Ilya Gutkovskiy_, Oct 01 2019