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A258424 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.

%I A258424 #5 May 29 2015 16:20:48
%S A258424 60949324800,11504185056000,1238502000960000,100203614366688000,
%T A258424 6786584967157027200,406962991813415247000,22343812436173975084800,
%U A258424 1147985274106305649476000,56030531363859577353444000,2626132408521540739815456000,119149819949135773678717267200
%N A258424 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 A258424 Alois P. Heinz, <a href="/A258424/b258424.txt">Table of n, a(n) for n = 10..600</a>
%p A258424 b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A258424        A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p A258424     end:
%p A258424 A:= proc(n, k) option remember; `if`(n=0, 1,
%p A258424       -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p A258424     end:
%p A258424 T:= proc(n, k) option remember;
%p A258424       add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p A258424     end:
%p A258424 a:= n-> T(n, 10):
%p A258424 seq(a(n), n=10..25);
%Y A258424 Column k=10 of A255982.
%K A258424 nonn
%O A258424 10,1
%A A258424 _Alois P. Heinz_, May 29 2015