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Number of bipartite partitions.
(Formerly M4359 N1827)
0

%I M4359 N1827 #19 Oct 20 2023 10:06:05

%S 7,18,44,88,169,296,507,824,1314,2029,3083,4578,6714,9676,13795,19408,

%T 27053,37302,51029,69180,93139,124447,165259,218021,286068,373207,

%U 484512,625845,804840,1030369,1313823,1668466,2111101,2661365,3343811,4187191

%N Number of bipartite partitions.

%D M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 11.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. S. Cheema and H. Gupta, <a href="/A002755/a002755.pdf">Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956</a>. (Annotated scanned pages from, plus a review)

%p nmax := 35:

%p gf := (n, m, k) -> 1/(product(product(1-x^r*y^t, t=k..m), r=0..n) * product(1-x^s, s=1..n)):

%p seq(coeff(coeff(series(series(gf(nmax, 8, 2), x, nmax+1), y, 9), y, 8), x, n), n=0..nmax); # _Sean A. Irvine_, Aug 14 2014

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Aug 14 2014