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%I A143563 #2 Mar 30 2012 18:37:11
%S A143563 1,1,6,29,242,1554,14476,104061,1024122,7818662,79523444,630256402,
%T A143563 6552401972,53271202948,562560238232,4658979320605,49780348483530,
%U A143563 418091057783582,4508111500966628,38281314209625862,415790041176520092
%N A143563 G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^2.
%F A143563 G.f. satisfies: A(x) + A(-x) = 1 + A(x)*A(-x) + x^2*A(x)^2*A(-x)^2.
%e A143563 G.f. A(x) = 1 + x + 6*x^2 + 29*x^3 + 242*x^4 + 1554*x^5 + 14476*x^6 +...
%e A143563 A(x)*A(-x) = 1 + 11*x^2 + 462*x^4 + 27907*x^6 + 1982266*x^8 +...
%e A143563 A(x)^2*A(-x)^2 = 1 + 22*x^2 + 1045*x^4 + 65978*x^6 + 4791930*x^8 +...
%o A143563 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^4/subst(A^2,x,-x));polcoeff(A,n)}
%K A143563 nonn
%O A143563 0,3
%A A143563 _Paul D. Hanna_, Aug 24 2008

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