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%I #4 Jun 04 2012 13:14:20
%S 1,1,12,72,1012,9552,148764,1609496,26398020,305821344,5174354988,
%T 62479377384,1079265357204,13399747245040,234917433809724,
%U 2975608178304696,52748683164797668,678307369324850496
%N G.f. satisfies: A(x) = 1 + x*A(x)^6/A(-x)^6.
%F G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
%F G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^6/A(-x)^5.
%F G.f. satisfies: (A(x) - 1)^5 = ( 1 - (1+x^2)/A(x) )^6/x = x^5*A(x)^30/A(-x)^30.
%F G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^6/G(-x)^5.
%e G.f. A(x) = 1 + x + 12*x^2 + 72*x^3 + 1012*x^4 + 9552*x^5 + 148764*x^6 +...
%e A(x)/A(-x) = 1 + 2*x + 2*x^2 + 122*x^3 + 242*x^4 + 16002*x^5 + 38962*x^6 +...
%e A(x)^5/A(-x)^5 = 1 + 10*x + 50*x^2 + 770*x^3 + 6450*x^4 + 109802*x^5 +...
%e where 1 - (1+x^2)/A(x) = x*A(x)^5/A(-x)^5.
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^6/subst(A^6,x,-x));polcoeff(A,n)}
%Y Cf. A143555, A143556, A143557, A143558.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2008
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