OFFSET
-1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of ( eta(q)^2 * eta(q^8)^3 / (eta(q^2)^3 * eta(q^16)^2))^2 in powers of q.
Euler transform of period 16 sequence [ -4, 2, -4, 2, -4, 2, -4, -4, -4, 2, -4, 2, -4, 2, -4, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (16 t)) = 4 * g(t) where q = exp(2 Pi i t) and g() is g.f. for A215348.
EXAMPLE
1/q - 4 + 8*q - 16*q^2 + 34*q^3 - 64*q^4 + 112*q^5 - 192*q^6 + 319*q^7 + ...
MATHEMATICA
QP = QPochhammer; s = (QP[q]^2*(QP[q^8]^3/(QP[q^2]^3*QP[q^16]^2)))^2 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 27 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( ( eta(x + A)^2 * eta(x^8 + A)^3 / (eta(x^2 + A)^3 * eta(x^16 + A)^2))^2, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 08 2012
STATUS
approved