OFFSET
0,7
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 + x - x^3 + x^4 + x^5 - 2*x^6 - 2*x^7 + 3*x^8 + 4*x^9 + ...
G.f. = 1/q + q^3 - q^11 + q^15 + q^19 - 2*q^23 - 2*q^27 + 3*q^31 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{-1, 1, 1, -2, 1, 1, -1, 0}[[Mod[k, 8, 1]]], {k, n}], {x, 0, n}]; (* Michael Somos, Jun 27 2017 *)
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; a:= CoefficientList[Series[f[-x^3, -x^5]^2/(f[-x, -x^3]*f[x^2, x^6]), {x, 0, 60}], x]]; 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, -1, 1, 1, -2, 1, 1, -1][k%8 + 1]), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 21 2014
STATUS
approved