A091437 Number of bipartite partitions of ceiling(n/2) white objects and floor(n/2) black ones.

1, 1, 2, 4, 9, 16, 31, 57, 109, 189, 339, 589, 1043, 1752, 2998, 4987, 8406, 13715, 22652, 36535, 59521, 94664, 151958, 239241, 379693, 591271, 927622, 1431608, 2224235, 3402259, 5236586, 7947530, 12130780, 18272221, 27669593, 41393154

Offset: 0

Author

Christian G. Bower, Jan 08 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

a(n) = A054225(n, [n/2]). Cf. A002774, A005380.

Programs

Mathematica

max = 35; se = Series[ Sum[ Log[1 - x^(n - k)*y^k], {n, 1, 2max}, {k, 0, n}], {x, 0, 2max}, {y, 0, 2max}]; coes = CoefficientList[ Series[ Exp[-se], {x, 0, 2max}, {y, 0, 2max}], {x, y}]; a[n_] := coes[[ Ceiling[(n+2)/2], Floor[(n+2)/2] ]]; Table[a[n], {n, 0, max} ](* Jean-François Alcover, Dec 06 2011 *)