A258423 - OEIS

%I #5 May 29 2015 16:22:16

%S 1764322560,268497815040,23638153069440,1582270134681600,

%T 89523597871058400,4521537191138385600,210558053896067770200,

%U 9231136974969952417200,386479930120038746283600,15609810973119409265234400,612788961533595085909010880,23513250306172521375772885440

%N Number of partitions of the 9-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="/A258423/b258423.txt">Table of n, a(n) for n = 9..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, 9):

%p seq(a(n), n=9..25);

%Y Column k=9 of A255982.

%K nonn

%O 9,1

%A _Alois P. Heinz_, May 29 2015