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A258420 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, such that each axis is used at least once.

%I A258420 #5 May 29 2015 16:25:47
%S A258420 95040,6308280,259518600,8563232700,249224561040,6703099068120,
%T A258420 171052924578480,4209175565848800,100941470303368480,
%U A258420 2376150752752629210,55182874193888254800,1268931845185709426820,28968880808493233206500,657875495503038733415880
%N A258420 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, such that each axis is used at least once.
%H A258420 Alois P. Heinz, <a href="/A258420/b258420.txt">Table of n, a(n) for n = 6..700</a>
%p A258420 b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A258420        A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p A258420     end:
%p A258420 A:= proc(n, k) option remember; `if`(n=0, 1,
%p A258420       -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p A258420     end:
%p A258420 T:= proc(n, k) option remember;
%p A258420       add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p A258420     end:
%p A258420 a:= n-> T(n, 6):
%p A258420 seq(a(n), n=6..25);
%Y A258420 Column k=6 of A255982.
%K A258420 nonn
%O A258420 6,1
%A A258420 _Alois P. Heinz_, May 29 2015