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%I #14 Apr 11 2019 04:09:53
%S 1,1,4,22,150,1198,10900,111392,1268816,16029676,223672208,3431679208,
%T 57595357568,1051552630592,20766322925296,441147381668704,
%U 10029896993061488,242949296094059648,6244343162806585552,169693360047016652048,4860575220802324411120,146335002352369970686352
%N G.f. A(x) satisfies: A(x) = Sum_{j>=0} j!*x^j*A(x)^j / Product_{k=1..j} (1 - k*x).
%H Vaclav Kotesovec, <a href="/A307439/b307439.txt">Table of n, a(n) for n = 0..250</a>
%F G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} k!*Stirling2(j,k)*A(x)^k.
%F a(n) ~ exp(1/2) * n! / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, Apr 10 2019
%e G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 150*x^4 + 1198*x^5 + 10900*x^6 + 111392*x^7 + 1268816*x^8 + 16029676*x^9 + 223672208*x^10 + ...
%t terms = 22; A[_] = 1; Do[A[x_] = Sum[j! x^j A[x]^j/Product[(1 - k x), {k, 1, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
%t terms = 22; A[_] = 1; Do[A[x_] = Sum[x^j Sum[k! StirlingS2[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
%Y Cf. A000670, A019538, A225293, A225294, A307402, A307440.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 08 2019
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