OFFSET
0,2
COMMENTS
Given g.f. A(x), then Q = A(-x^2) satisfies:
Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(3*k))/(1 + x*Q^(3*k))
due to a q-series expansion for the Jacobi theta_4 function.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 14*x^2 + 158*x^3 + 2274*x^4 + 37410*x^5 +...
where
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 + ...
PROG
(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)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 26 2012
STATUS
approved