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%I #6 Oct 29 2014 06:46:03
%S 1,1,1,3,7,21,60,181,557,1741,5531,17778,57741,189191,624634,2076037,
%T 6940372,23322865,78739090,266933783,908335157,3101467309,10622722567,
%U 36486959455,125652837052,433761554314,1500704852813,5202773031536,18072036054031,62886222829136,219194323393547
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (A(x) - x^k).
%H Vaclav Kotesovec, <a href="/A229188/b229188.txt">Table of n, a(n) for n = 0..160</a>
%F a(n) ~ c * d^n / n^(3/2), where d = 3.66153677891582..., c = 0.464274715544... . - _Vaclav Kotesovec_, Oct 29 2014
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 21*x^5 + 60*x^6 + 181*x^7 +...
%e where the g.f. A = A(x) satisfies:
%e A(x) = 1 + x*(A-x) + x^2*(A-x)*(A-x^2) + x^3*(A-x)*(A-x^2)*(A-x^3) + x^4*(A-x)*(A-x^2)*(A-x^3)*(A-x^4) + x^5*(A-x)*(A-x^2)*(A-x^3)*(A-x^4)*(A-x^5) +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*prod(k=1, m, A-x^k +x*O(x^n)))); polcoeff(A, n)}
%o for(n=0, 40, print1(a(n), ", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, Sep 15 2013
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