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A258423 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.

%I A258423 #5 May 29 2015 16:22:16
%S A258423 1764322560,268497815040,23638153069440,1582270134681600,
%T A258423 89523597871058400,4521537191138385600,210558053896067770200,
%U A258423 9231136974969952417200,386479930120038746283600,15609810973119409265234400,612788961533595085909010880,23513250306172521375772885440
%N A258423 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 A258423 Alois P. Heinz, <a href="/A258423/b258423.txt">Table of n, a(n) for n = 9..650</a>
%p A258423 b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A258423        A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p A258423     end:
%p A258423 A:= proc(n, k) option remember; `if`(n=0, 1,
%p A258423       -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p A258423     end:
%p A258423 T:= proc(n, k) option remember;
%p A258423       add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p A258423     end:
%p A258423 a:= n-> T(n, 9):
%p A258423 seq(a(n), n=9..25);
%Y A258423 Column k=9 of A255982.
%K A258423 nonn
%O A258423 9,1
%A A258423 _Alois P. Heinz_, May 29 2015