OFFSET
-1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..5000
FORMULA
Expansion of F(q) - 2 - 3 / F(q) in powers of q where F(q) = (eta(q^9)^2 / (eta(q^3) * eta(q^27)))^2.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (v - u^2) * (u - v^2) + 4 * (1 + u + v) * (u + v + u*v).
G.f. is a period 1 Fourier series which satisfies f(-1 / (81 t)) = f(t) where q = exp(2 Pi i t).
a(3*n) = 0 unless n = 0.
EXAMPLE
1/q - 2 - 3*q + 2*q^2 + 6*q^4 + 5*q^5 + 3*q^7 + 6*q^8 - 18*q^10 + 12*q^11 + ...
MATHEMATICA
QP = QPochhammer; F = (QP[q^9]^2/(QP[q^3]*QP[q^27]))^2; s = F - 2*q - 3*(q^2/F) + O[q]^70; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^9 + A)^2 / eta(x^3 + A) / eta(x^27 + A))^2; polcoeff( A - 2 * x - 3 * x^2 / A, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Dec 15 2008
STATUS
approved