OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
EXAMPLE
G.f. = 1 + 3*x + x^2 - 4*x^3 + 9*x^5 - x^6 - 20*x^7 + x^8 + 38*x^9 + ...
G.f. = 1/q + 3*q + q^3 - 4*q^5 + 9*q^9 - q^11 - 20*q^13 + q^15 + 38*q^17 + ...
MATHEMATICA
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; a:= CoefficientList[Series[(f[q, q]/f[q^2, q^2])*(f[-q^3, -q^5]/f[-q, -q^7]), {q, 0, 60}], q]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 06 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[0, -3, 5, -1, -2, -1, 5, -3][k%8 + 1]), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 21 2014
STATUS
approved