OFFSET
0,6
COMMENTS
g = Product_{m>=1} ((1-q^(8*m))*(1-q^(16*m)),
theta(t) = Sum_{n=-oo..oo} (q^(t*n^2)).
Although the OEIS does not normally include sequences in which only every fourth term is nonzero, this one is important enough to warrant an exception.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.
FORMULA
From G. C. Greubel, Jul 02 2018: (Start)
Expansion of eta(q^8)*eta(q^16)*theta_{3}(0, q^4)/q in powers of q.
Expansion of eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)). (End)
MAPLE
# This produces a list of the first 100 terms:
g:=q*mul((1-q^(8*m))*(1-q^(16*m)), m=1..30);
g:=series(g, q, 100);
th:=t->series( add(q^(t*n^2), n=-50..50), q, 100);
series(g*th(4), q, 100);
seriestolist(%);
MATHEMATICA
QP := QPochhammer; a:= CoefficientList[Series[QP[q^8]*QP[q^16]* EllipticTheta[3, 0, q^4], {q, 0, 60}], q]; Join[{0}, Table[a[[n]], {n, 1, 50}]] (* G. C. Greubel, Jul 02 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)); concat([0], Vec(A)) \\ G. C. Greubel, Jul 02 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Oct 18 2014
STATUS
approved