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%I #5 Oct 19 2019 12:05:16
%S 1,3,8,18,38,75,142,258,455,780,1308,2148,3467,5505,8618,13314,20327,
%T 30693,45882,67944,99745,145239,209882,301128,429148,607710,855414,
%U 1197228,1666585,2308014,3180668,4362762,5957444,8100192,10968478,14793954
%N Number of broken 1-diamond partitions of n.
%D Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI: broken diamonds and modular forms. Acta Arith. 126, 281-294 (2007)
%D 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.
%F 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) ).
%p Q := (a,q,M) -> mul(1-a*q^r, r=0..M-1);
%p Deltak := (k,M) -> Q(-q,q,M)/( Q(q,q,M)^2 * Q(-q^(2*k+1),q^(2*k+1),M) );
%p seriestolist(series(Deltak(1,64),q,40));
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 19 2019
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