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^(-2/3) * eta(q^3)^2 * eta(q^6)^2 / eta(q^2) in powers of q.
Euler transform of period 6 sequence [ 0, 1, -2, 1, 0, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = (2048/3)^(1/2) (t/I)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A263501.
a(n) = (-1)^n * A261444(n). a(8*n + 1) = 0.
EXAMPLE
G.f. = 1 + x^2 - 2*x^3 + 2*x^4 - 2*x^5 - 4*x^7 + 2*x^8 + x^10 - 4*x^11 + ...
G.f. = q^2 + q^8 - 2*q^11 + 2*q^14 - 2*q^17 - 4*q^23 + 2*q^26 + q^32 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] QPochhammer[ x^6]^3 / QPochhammer[ x^2], {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^6 + A)^2 / eta(x^2 + A), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 19 2015
STATUS
approved