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%I #6 Mar 30 2012 18:37:27
%S 1,1,2,5,11,26,64,158,399,1027,2675,7052,18788,50487,136711,372687,
%T 1021942,2816873,7800510,21691134,60543553,169561453,476351239,
%U 1342002198,3790565335,10732246631,30453309502,86589559266,246672752090
%N G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^(2*n-1)/(1 - x^(2*n-1)).
%C Related q-series identity:
%C Sum_{n>=1} y^n*z*q^(2*n-1)/(1-z*q^(2*n-1)) = Sum_{n>=1} z^n*y*q^n/(1-y*q^(2*n)); here q=x, y=A(x), z=1.
%F G.f. satisfies: A(x) = 1 + Sum_{n>=1} A(x)*x^n/(1 - A(x)*x^(2*n)).
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 11*x^4 + 26*x^5 + 64*x^6 +...
%e which satisfies the following relations:
%e A(x) = 1 + A(x)*x/(1-x) + A(x)^2*x^3/(1-x^3) + A(x)^3*x^5/(1-x^5) +...
%e A(x) = 1 + A(x)*x/(1-A(x)*x^2) + A(x)*x^2/(1-A(x)*x^4) + A(x)*x^3/(1-A(x)*x^6) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,A^m*x^(2*m-1)/(1-x^(2*m-1)+x*O(x^n))));polcoeff(A,n)}
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,A*x^m/(1-A*x^(2*m)+x*O(x^n))));polcoeff(A,n)}
%Y Cf. A192401, A192402.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 30 2011
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