OFFSET
0,2
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 f(-q, -q^2) / f(q, q^2) in powers of q where f(,) is Ramanujan's two-variable theta function.
Euler transform of period 6 sequence [ -2, -1, 0, -1, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 3^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A101195.
G.f.: Product_{k>0} (1 - x^k + x^(2*k)) / (1 + x^k + x^(2*k)).
a(n) = (-1)^n * A139137(n).
Convolution inverse is A098151.
EXAMPLE
G.f. = 1 - 2*q + 2*q^3 - 2*q^4 + 4*q^6 - 4*q^7 + 6*q^9 - 8*q^10 + 10*q^12 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] / 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 + A)^2 * eta(x^6 + A) / (eta(x^2 + A) * eta(x^3 + A)^2), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 04 2015
STATUS
approved