A258422 - OEIS

%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