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%I #3 Oct 26 2012 18:12:06
%S 1,2,14,158,2274,37410,670670,12786622,255519106,5302716866,
%T 113586849614,2501007496542,56446396937186,1303401799574242,
%U 30756416720161422,741216834445478270,18240706372460480002,458484823574294544770,11776969626284389958030
%N G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(3*n^2).
%C Given g.f. A(x), then Q = A(-x^2) satisfies:
%C Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(3*k))/(1 + x*Q^(3*k))
%C due to a q-series expansion for the Jacobi theta_4 function.
%e G.f.: A(x) = 1 + 2*x + 14*x^2 + 158*x^3 + 2274*x^4 + 37410*x^5 +...
%e where
%e A(x) = 1 + 2*x*A(x)^3 + 2*x^2*A(x)^12 + 2*x^3*A(x)^27 + 2*x^4*A(x)^48 + ...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, 2*x^m*(A+x*O(x^n))^(3*m^2))); polcoeff(A, n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A176719, A218294.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 26 2012
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