OFFSET
0,3
COMMENTS
Note that if G(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / G(x)^(n^2), then G(x) has negative coefficients.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 80*x^5 + 342*x^6 + 1818*x^7 + 11502*x^8 + 86626*x^9 + 707359*x^10 + 6202212*x^11 + 57655266*x^12 + ...
such that
A(x) = 1 + x*(1+x)^3/A(x) + x^2*(1+x)^12/A(x)^4 + x^3*(1+x)^27/A(x)^9 + x^4*(1+x)^48/A(x)^16 + x^5*(1+x)^75/A(x)^25 + x^6*(1+x)^108/A(x)^36 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(n=0, #A, x^n*(1+x +x*O(x^#A))^(4*n^2)/Ser(A)^(n^2+1) ), #A-1) ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 23 2018
STATUS
approved