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%I #4 Jun 04 2012 13:00:16
%S 1,1,7,31,273,1697,16471,116159,1186081,8928193,94017703,736522975,
%T 7917810225,63722594657,695248655095,5705316231551,62944217175617,
%U 524183926274433,5833380674885959,49141433498848159,550674827214221137
%N G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^3.
%F G.f. satisfies: A(x) + A(-x) = 1 + (1+x^2)*A(x)*A(-x).
%F G.f.: A(x) = G(x)/(1+x^2) where G(x) = 1 + x*G(x)^4/G(-x)^4 is the g.f. of A143557.
%e G.f. A(x) = 1 + x + 7*x^2 + 31*x^3 + 273*x^4 + 1697*x^5 +...
%e A(x)*A(-x) = 1 + 13*x^2 + 533*x^4 + 32409*x^6 + 2339753*x^8 +...
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^4/subst(A^3,x,-x));polcoeff(A,n)}
%Y Cf. A143557, A143562.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2008
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