A258424 - OEIS

%I #5 May 29 2015 16:20:48

%S 60949324800,11504185056000,1238502000960000,100203614366688000,

%T 6786584967157027200,406962991813415247000,22343812436173975084800,

%U 1147985274106305649476000,56030531363859577353444000,2626132408521540739815456000,119149819949135773678717267200

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

%H Alois P. Heinz, <a href="/A258424/b258424.txt">Table of n, a(n) for n = 10..600</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, 10):

%p seq(a(n), n=10..25);

%Y Column k=10 of A255982.

%K nonn

%O 10,1

%A _Alois P. Heinz_, May 29 2015