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 A307443 #8 Apr 10 2019 06:16:19
%S A307443 1,0,1,3,14,73,439,2986,22849,195639,1864072,19639587,227216485,
%T A307443 2866190328,39155468153,575750407431,9063067630294,152007287492665,
%U A307443 2705337486885751,50909087031293746,1009776468826520181,21052688394533433215,460223336063328374304,10525518902412521320567
%N A307443 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x)^(k+1).
%F A307443 G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} (-1)^(j-k)*k!*binomial(j,k)*A(x)^k.
%F A307443 a(n) ~ exp(-1) * n!. - _Vaclav Kotesovec_, Apr 10 2019
%e A307443 G.f.: A(x) = 1 + x^2 + 3*x^3 + 14*x^4 + 73*x^5 + 439*x^6 + 2986*x^7 + 22849*x^8 + 195639*x^9 + 1864072*x^10 + ...
%t A307443 terms = 24; A[_] = 1; Do[A[x_] = Sum[k! x^k A[x]^k/(1 + x)^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%t A307443 terms = 24; A[_] = 1; Do[A[x_] = Sum[x^j Sum[(-1)^(j - k) k! Binomial[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
%Y A307443 Cf. A000166, A088368, A307441, A307442, A307444.
%K A307443 nonn
%O A307443 0,4
%A A307443 _Ilya Gutkovskiy_, Apr 08 2019