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 A307444 #8 Apr 10 2019 06:15:45
%S A307444 1,0,1,2,11,54,336,2330,18359,161660,1580853,17031728,200718372,
%T A307444 2569989304,35531288796,527506796282,8368806193151,141271243571640,
%U A307444 2527897717923387,47789579768358498,951677263953890739,19910429474370487166,436589745454529328720,10012315468481417357976
%N A307444 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x*A(x))^(k+1).
%F A307444 G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000166(k)*x^k*A(x)^k.
%F A307444 G.f.: A(x) = (1/x)*Series_Reversion(x/Sum_{k>=0} A000166(k)*x^k).
%F A307444 a(n) ~ exp(-1) * n!. - _Vaclav Kotesovec_, Apr 10 2019
%e A307444 G.f.: A(x) = 1 + x^2 + 2*x^3 + 11*x^4 + 54*x^5 + 336*x^6 + 2330*x^7 + 18359*x^8 + 161660*x^9 + 1580853*x^10 + ...
%t A307444 terms = 24; CoefficientList[1/x InverseSeries[Series[x/Sum[Subfactorial[k] x^k, {k, 0, terms}], {x, 0, terms}], x], x]
%t A307444 terms = 24; A[_] = 1; Do[A[x_] = Sum[k! x^k A[x]^k/(1 + x A[x])^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%t A307444 terms = 24; A[_] = 1; Do[A[x_] = Sum[Subfactorial[k] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y A307444 Cf. A000166, A088368, A307441, A307442, A307443.
%K A307444 nonn
%O A307444 0,4
%A A307444 _Ilya Gutkovskiy_, Apr 08 2019