OFFSET
0,2
REFERENCES
George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016; http://www.personal.psu.edu/gea1/pdf/315.pdf
FORMULA
See Section 1 of Andrews (2016) or the Maple code below.
MAPLE
F:=(a, q, n)->mul(1-a*q^i, i=0..n-1); # This is (a; q)_n
M:=15;
# A098151:
THETA3:=(add((-1)^n*q^(3*n^2), n=-M..M)) /(add((-1)^n*q^(n^2), n=-M..M));
s1:=series(THETA3, q, 80); seriestolist(%);
# A275632:
THETABAR3:=1+2*add( (F(q, q, n-1)*q^(n^2)) / (F(q^n, q, n)*(1-q^n)), n=1..M);
s2:=series(THETABAR3, q, 80); seriestolist(%);
# A275633:
series((s1-s2)/8, q, 80);
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 09 2016
STATUS
editing