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A233896 G.f. satisfies: A(x) = 1 + x*A(x)^2*A(-x)^2 + x^2*(A(x)^2 + A(-x)^2).

%I A233896 #8 Dec 21 2013 13:40:51
%S A233896 1,1,2,6,10,33,72,236,572,1964,4800,16910,42354,150670,386992,1390176,
%T A233896 3622696,13128940,34580568,126131776,335409928,1229708169,3295834080,
%U A233896 12137093684,32738710652,121016095812,328220839472,1217132137132,3316783066620,12333770952588
%N A233896 G.f. satisfies: A(x) = 1 + x*A(x)^2*A(-x)^2 + x^2*(A(x)^2 + A(-x)^2).
%H A233896 Vaclav Kotesovec, <a href="/A233896/b233896.txt">Table of n, a(n) for n = 0..200</a>
%e A233896 G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 10*x^4 + 33*x^5 + 72*x^6 + 236*x^7 +...
%e A233896 Related series:
%e A233896 A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 36*x^4 + 110*x^5 + 286*x^6 + 868*x^7 +...
%e A233896 A(x)*A(-x) = 1 + 3*x^2 + 12*x^4 + 82*x^6 + 664*x^8 + 5479*x^10 + 47568*x^12 +...
%e A233896 A(x)^2*A(-x)^2 = 1 + 6*x^2 + 33*x^4 + 236*x^6 + 1964*x^8 + 16910*x^10 +...
%e A233896 A(x)^2+A(-x)^2 = 2 + 10*x^2 + 72*x^4 + 572*x^6 + 4800*x^8 + 42354*x^10 +...
%o A233896 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A^2*subst(A^2, x, -x)+x^2*(A^2+subst(A^2, x, -x+x*O(x^n))) ); polcoeff(A, n)}
%o A233896 for(n=0, 30, print1(a(n), ", "))
%Y A233896 Cf. A208887, A143926, A233895.
%K A233896 nonn
%O A233896 0,3
%A A233896 _Paul D. Hanna_, Dec 17 2013