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%I #4 Jul 06 2013 09:03:22
%S 1,1,1,3,5,10,23,44,93,193,398,828,1711,3548,7352,15238,31569,65414,
%T 135557,280856,581970,1205860,2498520,5177008,10726715,22225674,
%U 46051484,95417966,197704676,409640915,848768686,1758633069,3643854113
%N G.f.: A(x) = A_1 where A_1 = 1/[1 - x*(A_2)^2], A_2 = 1/[1 - x^2*(A_3)^2], A_3 = 1/[1 - x^3*(A_4)^2], ... A_n = 1/[1 - x^n*(A_{n+1})^2] for n>=1.
%F G.f.: 1/G(0) where G(k) = 1 - q^(k+1) / G(k+1)^2. [_Joerg Arndt_, Jul 06 2013]
%o (PARI) {a(n)=local(A=1+x*O(x^n)); for(j=0, n-1, A=1/(1-x^(n-j)*A^2 +x*O(x^n))); polcoeff(A, n)}
%o (PARI) N = 66; q = 'q + O('q^N);
%o G(k) = if(k>N, 1, 1 - q^(k+1) / G(k+1)^2 );
%o gf = 1 / G(0);
%o Vec(gf) \\ _Joerg Arndt_, Jul 06 2013
%Y Cf. A132333 (self-convolution); A132334 (variant).
%K nonn
%O 0,4
%A _Paul D. Hanna_, Aug 20 2007
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