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%I #2 Mar 30 2012 18:37:11
%S 1,1,2,14,50,432,1818,17082,77714,763967,3637718,36786268,180481258,
%T 1860798032,9324573430,97502825964,496344066386,5245970686152,
%U 27032002846992,288124627083382,1499144278319270,16087838913122064
%N G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^3.
%F G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^8.
%e G.f. A(x) = 1 + x + 2*x^2 + 14*x^3 + 50*x^4 + 432*x^5 + 1818*x^6 +...
%e Related expansions:
%e A(x)^5 = 1 + 5*x + 20*x^2 + 120*x^3 + 635*x^4 + 4301*x^5 + 25360*x^6 +...
%e A(-x)^3 = 1 - 3*x + 9*x^2 - 55*x^3 + 252*x^4 - 1818*x^5 + 9560*x^6 -+...
%e A(x)*A(-x) = 1 + 3*x^2 + 76*x^4 + 2776*x^6 + 118940*x^8 +...
%e [A(x)*A(-x)]^8 = 1 + 24*x^2 + 860*x^4 + 36488*x^6 + 1700198*x^8 +...
%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5*subst(A^3,x,-x));polcoeff(A,n)}
%Y Cf. A143550, A143551, A143552, A143554.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2008
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