OFFSET
0,3
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
Expansion of q^(-17/24) * eta(q^3)^2 * eta(q^4)^2 * eta(q^24) / (eta(q) * eta(q^8) * eta(q^12)) in powers of q.
Euler transform of period 24 sequence [ 1, 1, -1, -1, 1, -1, 1, 0, -1, 1, 1, -2, 1, 1, -1, 0, 1, -1, 1, -1, -1, 1, 1, -2, ...].
EXAMPLE
G.f. = 1 + x + 2*x^2 + x^3 + x^4 + x^5 + 2*x^7 + x^9 + x^10 + x^11 + ...
G.f. = q^17 + q^41 + 2*q^65 + q^89 + q^113 + q^137 + 2*q^185 + q^233 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^2 QPochhammer[ -x^2, x^4] / (QPochhammer[ x, x^2] QPochhammer[ x^12, x^24]), {x, 0, n}];
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] EllipticTheta[ 4, 0, x^4] EllipticTheta[ 2, Pi/4, x^3] / (x^(3/4) Sqrt[2] QPochhammer[ x]), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^2 * eta(x^4 + A)^2 * eta(x^24 + A) / (eta(x + A) * eta(x^8 + A) * eta(x^12 + A)), n))};
(PARI) q='q+O('q^99); Vec(eta(q^3)^2*eta(q^4)^2*eta(q^24)/(eta(q)*eta(q^8)*eta(q^12))) \\ Altug Alkan, Aug 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 27 2015
STATUS
approved