A002768 Number of bipartite partitions.

5, 13, 30, 59, 109, 187, 312, 497, 775, 1176, 1753, 2561, 3694, 5245, 7366, 10223, 14056, 19137, 25853, 34637, 46092, 60910, 80009, 104462, 135674, 175274

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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. 32.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• 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. (Annotated scanned pages from, plus a review)

Programs

Maple

nmax := 20:
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)):
seq(coeff(coeff(series(series(gf(nmax, 15, 5), x, nmax+1), y, 16), y, 15), x, n), n=0..nmax); # Sean A. Irvine, Aug 15 2014