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Number of bipartite partitions of ceiling(n/2) white objects and floor(n/2) black ones.
4

%I #12 Nov 16 2019 16:51:11

%S 1,1,2,4,9,16,31,57,109,189,339,589,1043,1752,2998,4987,8406,13715,

%T 22652,36535,59521,94664,151958,239241,379693,591271,927622,1431608,

%U 2224235,3402259,5236586,7947530,12130780,18272221,27669593,41393154

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

%H Alois P. Heinz, <a href="/A091437/b091437.txt">Table of n, a(n) for n = 0..100</a>

%t 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 *)

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

%K nonn

%O 0,3

%A _Christian G. Bower_, Jan 08 2004