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Number of partitions of the 10-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.
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%I #9 Mar 11 2019 06:43:56

%S 1,10,200,4955,137300,4074000,126608100,4068161370,134057837000,

%T 4505692837250,153860041920200,5322981634672000,186175022952887500,

%U 6572164280362285000,233857080811291255200,8379031938022660903665,302042773405644342524700

%N Number of partitions of the 10-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="/A237025/b237025.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..10} (-1)^i*C(10,i)*(G*x)^(2^(10-i)).

%Y Column k=10 of A237018.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 02 2014