OFFSET
0,4
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^(-1/6) * eta(q^3)^2 * eta(q^4) / eta(q^6) in powers of q.
Euler transform of period 12 sequence [ 0, 0, -2, -1, 0, -1, 0, -1, -2, 0, 0, -2, ...].
G.f.: (Sum_{k in Z} (-1)^k * x^(3*k^2)) * Product_{k>0} (1 - x^(4*k)).
EXAMPLE
1 - 2*x^3 - x^4 + 2*x^7 - x^8 + 2*x^11 + 2*x^12 - 2*x^16 - x^20 - 2*x^23 + ...
q - 2*q^19 - q^25 + 2*q^43 - q^49 + 2*q^67 + 2*q^73 - 2*q^97 - q^121 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^3] QPochhammer[ q^4], {q, 0, n}]
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^2 * eta(x^4 + A) / eta(x^6 + A), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jun 20 2013
STATUS
approved