OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-7/8) * eta(q)^2 * eta(q^6)^5 / (eta(q^2) * eta(q^3)^3) in powers of q.
Euler transform of period 6 sequence [ -2, -1, 1, -1, -2, -3, ...].
a(3*n + 2) = a(27*n + 25) = 0.
EXAMPLE
1 - 2*x + 3*x^3 - 4*x^4 + 4*x^6 - 2*x^7 + 5*x^9 - 6*x^10 + 5*x^12 - 8*x^13 + ...
q^7 - 2*q^15 + 3*q^31 - 4*q^39 + 4*q^55 - 2*q^63 + 5*q^79 - 6*q^87 + 5*q^103 + ...
MATHEMATICA
a[n_]:= SeriesCoefficient[EllipticTheta[3, 0, -x]*EllipticTheta[2, 0, x^(3/2)]^2/(4*x^(3/4)*QPochhammer[x^3, x^6]), {x, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Dec 08 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^6 + A)^5 / (eta(x^2 + A) * eta(x^3 + A)^3), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 17 2013
STATUS
approved