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A328543
Number of 5 dots bracelet partitions of n.
0
1, 5, 19, 60, 169, 435, 1050, 2400, 5250, 11060, 22562, 44740, 86539, 163695, 303500, 552560, 989460, 1745025, 3034670, 5209240, 8834663, 14815240, 24583588, 40390560, 65745538, 106079820, 169741260, 269475500, 424621150, 664344055
OFFSET
0,2
REFERENCES
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 k dots bracelet partitions of n is Q(-q,q,oo)/( Q(q,q,oo)^(k-1) * Q(-q^k,q^k,oo) ).
MAPLE
Q := (a, q, M) -> mul(1-a*q^r, r=0..M-1);
BBBk := (k, M) -> Q(-q, q, M)/( Q(q, q, M)^(k-1) * Q(-q^k, q^k, M) );
seriestolist(series(BBBk(5, 64), q, 40));
CROSSREFS
Sequence in context: A332720 A092442 A341711 * A135266 A124123 A189714
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2019
STATUS
approved