%I #6 Apr 30 2014 01:34:07
%S 1,-2,-2,-16,14,64,-484,-2048,3798,-7168,96292,131072,-1247476,
%T 3964928,-27170632,-67108864,220816742,-497811456,993377620,
%U -3758096384,38457826404,-201938960384,1217833409416,1099511627776,-4275253627140
%N Coefficients of the solution to a functional equation.
%C G.f. A(x) satisfies A(-4x^2)=A(x)+A(-x), A(4x^2)=-4A(x)A(-x).
%F a(n)*(-4)^n = 2*a(2n) - _Paul D. Hanna_, Apr 04 2004
%F Given g.f. A(x), then B(x)=4A(x/4) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=u^2v+uw-v^2.
%F Given g.f. A(x), then B(x)=4A(x/4) satisfies B(-x^2)=B(x)+B(-x) and B(x^2)=-B(x)*B(-x).
%o (PARI) a(n)=local(A,A2,m); if(n<1,0,A=x+O(x^2); m=1; while(m<=n,m*=2; A2=subst(A,x,-x^2); A=A2/2+sqrt(A2^2/4+subst(A,x,x^2))); polcoeff(A,n)*4^(n-1))
%K sign
%O 1,2
%A _Michael Somos_, Mar 20 2004