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%I #14 Apr 11 2019 04:10:23
%S 1,1,3,14,86,647,5739,58647,679513,8818219,126887789,2007051456,
%T 34634864692,647737588429,13052029344893,281915983915202,
%U 6497718168838214,159172833649907801,4129605445474716345,113112957674428539930,3261790879443599064394,98772906841120521388973
%N G.f. A(x) satisfies: A(x) = Sum_{j>=0} j!*x^j / Product_{k=1..j} (1 - k*x*A(x)).
%H Vaclav Kotesovec, <a href="/A307440/b307440.txt">Table of n, a(n) for n = 0..258</a>
%F G.f. satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} k!*Stirling2(j,k)*A(x)^(j-k).
%F a(n) ~ exp(-1/2) * n! / (log(2))^(n+1). - _Vaclav Kotesovec_, Apr 10 2019
%e G.f.: A(x) = 1 + x + 3*x^2 + 14*x^3 + 86*x^4 + 647*x^5 + 5739*x^6 + 58647*x^7 + 679513*x^8 + 8818219*x^9 + 126887789*x^10 + ...
%t terms = 22; A[_] = 1; Do[A[x_] = Sum[j! x^j/Product[(1 - k x A[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]^(j - k), {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
%Y Cf. A000670, A019538, A225293, A225294, A307402, A307439.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 08 2019
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