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 q^(-1/2) * eta(q^2)^7 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)^4) in powers of q.
Euler transform of period 8 sequence [ 2, -5, 2, -1, 2, -5, 2, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (64 t)) = 32 (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A246835.
EXAMPLE
G.f. = 1 + 2*x - 2*x^2 - 4*x^3 + 3*x^4 + 2*x^5 - 6*x^6 - 4*x^7 + 4*x^8 + ...
G.f. = q + 2*q^3 - 2*q^5 - 4*q^7 + 3*q^9 + 2*q^11 - 6*q^13 - 4*q^15 + 4*q^17 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, Pi/4, x]^2 EllipticTheta[ 3, 0, x] / (2 x^(1/2)), {x, 0, n}];
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^8 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^4), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 04 2014
STATUS
approved