OFFSET
0,2
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^(-2/3) * eta(q)^2 * eta(q^2)^6 * eta(q^12)^2 / (eta(q^4)^4 * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [-2, -8, -2, -4, -2, -7, -2, -4, -2, -8, -2, -5, ...].
8 * a(n) = A245643(3*n + 2).
EXAMPLE
G.f. = 1 - 2*x - 7*x^2 + 14*x^3 + 20*x^4 - 36*x^5 - 34*x^6 + 40*x^7 + ...
G.f. = q^2 - 2*q^5 - 7*q^8 + 14*q^11 + 20*q^14 - 36*q^17 - 34*q^20 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2]^6 EllipticTheta[ 2, 0, x^3] / (2 x^(3/4) QPochhammer[ -x]^2), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A)^6 * eta(x^12 + A)^2 / (eta(x^4 + A)^4 * eta(x^6 + A)), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^2)^6*eta(q^12)^2/(eta(q^4)^4*eta(q^6))) \\ Altug Alkan, Jul 31 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 16 2015
STATUS
approved