OFFSET
0,3
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 eta(q^4)^5 * eta(q^6) / (eta(q^2)^2 * eta(q^3)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 24 sequence [ 0, 2, 2, -3, 0, 3, 0, -1, 2, 2, 0, -2, 0, 2, 2, -1, 0, 3, 0, -3, 2, 2, 0, 0, ...].
a(n) = A143068(2*n). a(3*n + 1) = 0.
EXAMPLE
G.f. = 1 + 2*q^2 + 2*q^3 + 4*q^5 + 4*q^6 + 10*q^8 + 8*q^9 + 20*q^11 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^2] / EllipticTheta[ 4, 0, q^3], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^5 * eta(x^6 + A) / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^8 + A)^2), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 09 2015
STATUS
approved