%N Mutual solutions to two classification counting problems: binary block codes of wordlength J with N used words; and classifications of N elements by J partitions.
%C This connection was conjectured by _Robert Munafo_, then proved by _Andrew Weimholt_.
%C A(n) counts 2-colorings of a J-dimensional hypercube with N red vertices and 2^J-N black, each edge has at most one red vertex. - _Andrew Weimholt_, Dec 30 2009
%C This sequence contains terms of A039754 that are found in A171871/A171872. They occur in blocks of length 2^(J-1) as shown here:
%H Harald Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/html2/construction/blockcodes_2.html">Enumeration of block codes</a>
%H R. Munafo, <a href="http://mrob.com/pub/math/seq-a005646.html">Classifications of N Elements</a>
%Y Cf. A039754, A171872, A171871, A005646.
%A _Robert Munafo_, Jan 21 2010