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A258421 Number of partitions of the 7-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 A258421 #5 May 29 2015 16:24:39
%S A258421 2162160,196756560,10778727960,463305056760,17266750912320,
%T A258421 586609859314080,18699578507549520,569565504689176800,
%U A258421 16777853060738524020,482011338862966969980,13586929812483090607600,377442353035435719228120,10367784656620152180344310
%N A258421 Number of partitions of the 7-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 A258421 Alois P. Heinz, <a href="/A258421/b258421.txt">Table of n, a(n) for n = 7..700</a>
%p A258421 b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A258421        A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p A258421     end:
%p A258421 A:= proc(n, k) option remember; `if`(n=0, 1,
%p A258421       -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p A258421     end:
%p A258421 T:= proc(n, k) option remember;
%p A258421       add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p A258421     end:
%p A258421 a:= n-> T(n, 7):
%p A258421 seq(a(n), n=7..25);
%Y A258421 Column k=7 of A255982.
%K A258421 nonn
%O A258421 7,1
%A A258421 _Alois P. Heinz_, May 29 2015