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%I #9 Mar 30 2012 18:37:34
%S 1,1,2,5,16,63,329,2291,21986,293295,5493212,145199609,5435890215,
%T 288986265721,21854960540507,2354333160724935,361635116847622331,
%U 79267245693976433777,24809117584333459025386,11092978451251892467436829,7089163369051891054753027252
%N G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(n*x^d/d) ).
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 63*x^5 + 329*x^6 +...
%e By definition:
%e log(A(x)) = x*A(x) + x^2*A(2*x)*A(x^2)/2 + x^3*A(3*x)*A(x^3)/3 + x^4*A(4*x)*A(2*x^2)*A(x^4)/4 + x^5*A(5*x)*A(x^5)/5 + x^6*A(6*x)*A(3*x^2)*A(2*x^3)*A(x^6)/6 +...
%e Explicitly,
%e log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 221*x^5/5 + 1506*x^6/6 + 13196*x^7/7 + 153979*x^8/8 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n+1,x^m/m*exp(sumdiv(m,d,log(subst(A,x,m*x^d/d +x*O(x^n))))))));polcoeff(A,n)}
%Y Cf. A205499, A205500, A205501, A205502.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 27 2012
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