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%I #6 Jun 04 2012 13:10:32
%S 1,1,8,32,280,1728,16744,117856,1202552,9044352,95203784,745451168,
%T 8011827928,64459117632,703166465320,5769038826208,63639465830712,
%U 529889242505984,5896324892061576,49665617425122592,556508207889107096
%N G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^4.
%F G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
%F G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^4 / A(-x)^3.
%F G.f. satisfies: (A(x) - 1)^3 = ( 1 - (1+x^2)/A(x) )^4/x = x^3*A(x)^12/A(-x)^12.
%F G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^4/G(-x)^3 is the g.f. of A143564.
%e G.f. A(x) = 1 + x + 8*x^2 + 32*x^3 + 280*x^4 + 1728*x^5 + 16744*x^6 +...
%e A(x)/A(-x) = 1 + 2*x + 2*x^2 + 50*x^3 + 98*x^4 + 2658*x^5 + 6370*x^6 +...
%e A(x)^3/A(-x)^3 = 1 + 6*x + 18*x^2 + 182*x^3 + 930*x^4 + 10374*x^5 +...
%e where 1 - (1+x^2)/A(x) = x*A(x)^3/A(-x)^3.
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^4/subst(A^4,x,-x));polcoeff(A,n)}
%Y Cf. A143564, A143555, A143556, A143558, A143559.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2008
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