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 phi(-x) * f(x^1, x^5) in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of q^(-1/3) * eta(q) * eta(q^2) * eta(q^3) * eta(q^12) / (eta(q^4) * eta(q^6)) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 768^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A246838.
a(n) = (-1)^n * A246650(n).
EXAMPLE
G.f. = 1 - x - 2*x^2 + 2*x^4 + 3*x^5 - 2*x^6 + x^8 - 2*x^9 - 2*x^10 + ...
G.f. = q - q^4 - 2*q^7 + 2*q^13 + 3*q^16 - 2*q^19 + q^25 - 2*q^28 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x] QPochhammer[ x^2] QPochhammer[ x^3] QPochhammer[ x^12] / (QPochhammer[ x^4] QPochhammer[ x^6]), {x, 0, n}];
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] QPochhammer[ -x, x^6] QPochhammer[ -x^5, x^6] QPochhammer[ x^6], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A) / (eta(x^4 + A) * eta(x^6 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 02 2014
STATUS
approved