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%I #5 May 29 2015 16:23:21
%S 57657600,6895848960,485566099200,26364414061440,1224007231940640,
%T 51216101151626880,1991943704397427200,73440737647137519120,
%U 2601107886874207253760,89332305977055996111040,2995343867463073686769440,98555316817167057069129600
%N Number of partitions of the 8-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 Alois P. Heinz, <a href="/A258422/b258422.txt">Table of n, a(n) for n = 8..650</a>
%p b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p end:
%p A:= proc(n, k) option remember; `if`(n=0, 1,
%p -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p end:
%p T:= proc(n, k) option remember;
%p add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p end:
%p a:= n-> T(n, 8):
%p seq(a(n), n=8..25);
%Y Column k=8 of A255982.
%K nonn
%O 8,1
%A _Alois P. Heinz_, May 29 2015
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