OFFSET
0,2
REFERENCES
Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI: broken diamonds and modular forms. Acta Arith. 126, 281-294 (2007)
Cui, Su-Ping, and Nancy SS Gu. "Congruences for broken 3-diamond and 7 dots bracelet partitions." The Ramanujan Journal 35.1 (2014): 165-178.
FORMULA
We write (a;q)_M as Q(a,q,M). The g.f. for the number of broken k-diamond partitions of n is Q(-q,q,oo)/( Q(q,q,oo)^2 * Q(-q^(2*k+1),q^(2*k+1),oo) ).
MAPLE
Q := (a, q, M) -> mul(1-a*q^r, r=0..M-1);
Deltak := (k, M) -> Q(-q, q, M)/( Q(q, q, M)^2 * Q(-q^(2*k+1), q^(2*k+1), M) );
seriestolist(series(Deltak(3, 64), q, 40));
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2019
STATUS
approved