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%I #10 Nov 04 2018 08:57:51
%S 1,1,2,3,6,8,15,20,35,48,76,103,166,221,333,451,671,894,1303,1730,
%T 2479,3288,4615,6086,8502,11142,15299,20034,27285,35514,47937,62168,
%U 83259,107650,142929,184090,243207,312041,409210,523709,683261,871239,1130703
%N G.f. satisfies: A(x) = 1/(1-x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*...
%H Seiichi Manyama, <a href="/A129374/b129374.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: A(x) = Product_{n>=1} 1/(1 - x^n)^A074206(n) where A074206(n) equals the number of ordered factorizations of n.
%F a(n) ~ exp((1 + 1/r) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(1+r)) * n^(r/(1+r))) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(10*(1+r))) / ((2*Pi)^(29/50) * sqrt(1+r) * n^((6 + 5*r)/(10*(1+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/(1-x)*prod(n=2,i,subst(A,x,x^n+x*O(x^i)))); polcoeff(A,n)}
%Y Cf. A074206, A129373, A129375.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 12 2007
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