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%I #6 Mar 11 2019 06:43:01
%S 1,6,72,1065,17604,311472,5770692,110530514,2171011800,43490709702,
%T 885138113016,18250712631216,380432844142092,8003697071972760,
%U 169728054535951520,3624215619984643650,77857888349211858000,1681568232191988128040,36491768084579204728800
%N Number of partitions of the 6-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.
%H Alois P. Heinz, <a href="/A237021/b237021.txt">Table of n, a(n) for n = 0..300</a>
%H Yu Hin (Gary) Au, Fatemeh Bagherzadeh, Murray R. Bremner, <a href="https://arxiv.org/abs/1903.00813">Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube</a>, arXiv:1903.00813 [math.CO], Mar 03 2019.
%F G.f. G satisfies: x = Sum_{i=0..6} (-1)^i*C(6,i)*(G*x)^(2^(6-i)).
%Y Column k=6 of A237018.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Feb 02 2014