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%I #6 Jun 04 2012 13:13:33
%S 1,1,10,50,570,4450,56202,501970,6676410,63799490,875391370,
%T 8715058802,122088479930,1249437863970,17764858122250,185445650940690,
%U 2666213981716282,28252030821781890,409717783914784010
%N G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x)^5.
%F G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
%F G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^5/A(-x)^4.
%F G.f. satisfies: (A(x) - 1)^4 = ( 1 - (1+x^2)/A(x) )^5/x = x^4*A(x)^20/A(-x)^20.
%F G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^5/G(-x)^4.
%e G.f. A(x) = 1 + x + 10*x^2 + 50*x^3 + 570*x^4 + 4450*x^5 + 56202*x^6 +...
%e A(x)/A(-x) = 1 + 2*x + 2*x^2 + 82*x^3 + 162*x^4 + 7202*x^5 + 17442*x^6 +...
%e A(x)^4/A(-x)^4 = 1 + 8*x + 32*x^2 + 408*x^3 + 2752*x^4 + 38760*x^5 +...
%e where 1 - (1+x^2)/A(x) = x*A(x)^4/A(-x)^4.
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5/subst(A^5,x,-x));polcoeff(A,n)}
%Y Cf. A143555, A143556, A143557, A143559.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2008
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