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%I #2 Mar 30 2012 18:37:11
%S 1,1,1,3,19,297,8953,572155,72116459,18460128753,9414877745601,
%T 9640779710687955,19725063387945457219,80793830752052788593529,
%U 661701532957780822275151305,10841317673677535233876159099755
%N G.f. satisfies: A(x) = 1 + x*A(2x)*A(-x).
%F G.f. satisfies: A(x) = (1 + x*A(2x))/(1 + x^2*A(2x)*A(-2x)).
%F a(n) = Sum_{k=0..n-1} 2^k*(-1)^(n-1-k)*a(k)*a(n-1-k) for n>0 with a(0)=1.
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 19*x^4 + 297*x^5 + 8953*x^6 +...
%e A(x) = 1 + x*A(2x)*[1 - x*A(-2x)*[1 + x*A(2x)*[1 - x*A(-2x)*[1 +...]]]].
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,2*x)*subst(A,x,-x));polcoeff(A,n)}
%o (PARI) {a(n)=if(n==0,1,sum(k=0,n-1,2^k*(-1)^(n-1-k)*a(k)*a(n-1-k)))}
%K nonn
%O 0,4
%A _Paul D. Hanna_, Aug 28 2008
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