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%I #6 Mar 30 2012 18:37:26
%S 1,1,2,5,12,33,92,267,792,2403,7414,23199,73454,234901,757654,2461877,
%T 8051284,26480681,87534184,290652931,968992200,3242229475,10884245838,
%U 36648566551,123739675390,418848744517,1421072269234,4831811596381
%N G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A006519(n) where A006519(n) = highest power of 2 dividing n.
%F G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=0} x^(2^n)*A(x)^(2^n)/(1 - x^(2^(n+1))).
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 33*x^5 + 92*x^6 + 267*x^7 +...
%e The g.f. satisfies the following relations:
%e A(x) = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x) + x^4*A(x)^4 + x^5*A(x) + x^6*A(x)^2 + x^7*A(x) + x^8*A(x)^8 +...+ x^n*A(x)^A006519(n) +...
%e A(x) = 1 + x*A(x)/(1-x^2) + x^2*A(x)^2/(1-x^4) + x^4*A(x)^4/(1-x^8) + x^8*A(x)^8/(1-x^16) + x^16*A(x)^16/(1-x^32) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(2^valuation(m,2))));polcoeff(A,n)}
%Y Cf. A191768.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 16 2011
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