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 A318365 #11 Jan 09 2019 09:15:55
%S A318365 1,1,1,4,21,116,805,6504,59353,608320,6901641,85824080,1160786341,
%T A318365 16959401304,266133942061,4463567862376,79669223849265,
%U A318365 1507610621184224,30145968665822737,635066714078714016,14057275047440540221,326159212986987669640,7915118313077599105461,200503241124736099689656
%N A318365 Expansion of e.g.f. exp(x*exp(-x)/(1 - x)).
%F A318365 a(0) = 1; a(n) = Sum_{k=1..n} A000240(k)*binomial(n-1,k-1)*a(n-k).
%F A318365 a(n) ~ exp(exp(-1)/2 - 1/4 + 2*exp(-1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - _Vaclav Kotesovec_, Aug 25 2018
%p A318365 seq(n!*coeff(series(exp(x*exp(-x)/(1-x)),x=0,24),x,n),n=0..23); # _Paolo P. Lava_, Jan 09 2019
%t A318365 nmax = 23; CoefficientList[Series[Exp[x Exp[-x]/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
%t A318365 a[n_] := a[n] = Sum[k Subfactorial[k - 1] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
%o A318365 (PARI) x = 'x + O('x^25); Vec(serlaplace(exp(x*exp(-x)/(1 - x)))) \\ _Michel Marcus_, Aug 25 2018
%Y A318365 Cf. A000166, A000240, A000262, A003725, A318364.
%K A318365 nonn
%O A318365 0,4
%A A318365 _Ilya Gutkovskiy_, Aug 24 2018