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%I #3 Jul 14 2012 15:15:06
%S 1,1,2,5,14,77,272,954,3390,20942,81886,313216,1200192,7744531,
%T 31604104,125795060,500225166,3302458490,13797942732,56190743623,
%U 228422293810,1529418005565,6486104136768,26809045163856,110586420610480,747542548312112,3203080302079898
%N G.f. satisfies: A(x) = 1 + x*A(x)^3*A(-x)*A(I*x)*A(-I*x).
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 77*x^5 + 272*x^6 + 954*x^7 +...
%e Related expansions:
%e A(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 202*x^5 + 779*x^6 + 2900*x^7 +...
%e A(x)^3 = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 402*x^5 + 1631*x^6 + 6372*x^7 +...
%e A(x)*A(-x) = 1 + 3*x^2 + 22*x^4 + 421*x^6 + 5386*x^8 + 127595*x^10 +...
%e A(x)*A(-x)*A(I*x)*A(-I*x) = 1 + 35*x^4 + 8730*x^8 + 3122301*x^12 + 1308019950*x^16 + 599139933987*x^20 + 290661820794000*x^24 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*A^3*subst(A,x,-x)*subst(A,x,I*x)*subst(A,x,-I*x));polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A118968.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 14 2012
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