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%I #9 Nov 04 2018 09:14:10
%S 1,1,1,2,3,4,7,9,13,19,26,34,52,67,89,123,166,214,295,380,501,660,858,
%T 1098,1461,1858,2384,3072,3940,4975,6410,8070,10234,12946,16322,20412,
%U 25848,32201,40261,50287,62728,77681,96885,119673,148197,183108,225974
%N G.f. satisfies: A(x) = (1+x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*...
%H Seiichi Manyama, <a href="/A129373/b129373.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: A(x) = Product_{n>=1} (1 + x^n)^A074206(n) where A074206(n) equals the number of ordered factorizations of n.
%F a(n) ~ exp((1 + 1/r) * (-(1 - 2^(-r)) * Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(1+r)) * n^(r/(1+r))) * (-(1 - 2^(-r)) * Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(2 + 2*r)) / (2^(1/10) * sqrt(Pi) * sqrt(1+r) * n^((2+r)/(2 + 2*r))), where r = A107311 = 1.7286472389981836181351... is the root of the equation Zeta(r) = 2, Zeta'(r) = -1/A247667. - _Vaclav Kotesovec_, Nov 04 2018
%o (PARI) {a(n)=local(A=1+x);for(i=2,n,A=(1+x)*prod(n=2,i,subst(A,x,x^n+x*O(x^i)))); polcoeff(A,n)}
%Y Cf. A074206; A129374, A129375.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Apr 12 2007