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A191768 G.f. a(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A000265(n) where A000265(n) = largest odd divisor of n.

%I A191768 #6 Mar 30 2012 18:37:26
%S A191768 1,1,2,4,10,25,68,193,565,1688,5136,15854,49517,156191,496836,1591924,
%T A191768 5133091,16643856,54234349,177505376,583272256,1923482331,6363842492,
%U A191768 21117432227,70265970878,234388421515,783664894313,2625748635300
%N A191768 G.f. a(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A000265(n) where A000265(n) = largest odd divisor of n.
%F A191768 G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=0} x^(2^n)*A(x)/(1 - x^(2*2^n)*A(x)^2).
%e A191768 G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 68*x^6 + 193*x^7 +...
%e A191768 The g.f. satisfies the following identities:
%e A191768 A(x) = 1 + x*A(x) + x^2*A(x) + x^3*A(x)^3 + x^4*A(x) + x^5*A(x)^5 + x^6*A(x)^3 + x^7*A(x)^7 + x^8*A(x) +...+ x^n*A(x)^A000265(n) +...
%e A191768 A(x) = 1 + x*A(x)/(1-x^2*A(x)^2) + x^2*A(x)/(1-x^4*A(x)^2) + x^4*A(x)/(1-x^8*A(x)^2) + x^8*A(x)/(1-x^16*A(x)^2) +...
%o A191768 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(m/2^valuation(m,2))));polcoeff(A,n)}
%Y A191768 Cf. A191769.
%K A191768 nonn
%O A191768 0,3
%A A191768 _Paul D. Hanna_, Jun 16 2011