OFFSET
0,11
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-1/4) * eta(q) * eta(q^12) / (eta(q^3) * eta(q^4)) in powers of q.
Euler transform of period 12 sequence [-1, -1, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (192 t)) = f(t) where q = exp(2 Pi i t).
Convolution inverse of A112192.
EXAMPLE
G.f. = 1 - x - x^2 + x^3 - x^5 + x^6 + x^9 - 2*x^10 + 3*x^12 + ...
G.f. = q - q^3 - q^5 + q^7 - q^11 + q^13 + q^19 - 2*q^21 + 3*q^25 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x] QPochhammer[ x^12] / (QPochhammer[ x^3] QPochhammer[ x^4]), {x, 0, n}];
eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(-1/4)* eta[q]*eta[q^12]/(eta[q^3]*eta[q^4]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A) / (eta(x^3 + A) * eta(x^4 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 30 2015
STATUS
approved