cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A091437 #12 Nov 16 2019 16:51:11
%S A091437 1,1,2,4,9,16,31,57,109,189,339,589,1043,1752,2998,4987,8406,13715,
%T A091437 22652,36535,59521,94664,151958,239241,379693,591271,927622,1431608,
%U A091437 2224235,3402259,5236586,7947530,12130780,18272221,27669593,41393154
%N A091437 Number of bipartite partitions of ceiling(n/2) white objects and floor(n/2) black ones.
%H A091437 Alois P. Heinz, <a href="/A091437/b091437.txt">Table of n, a(n) for n = 0..100</a>
%t A091437 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 A091437 a(n) = A054225(n, [n/2]). Cf. A002774, A005380.
%K A091437 nonn
%O A091437 0,3
%A A091437 _Christian G. Bower_, Jan 08 2004