cp's OEIS Frontend

A258422 Number of partitions of the 8-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 A258422 #5 May 29 2015 16:23:21
%S A258422 57657600,6895848960,485566099200,26364414061440,1224007231940640,
%T A258422 51216101151626880,1991943704397427200,73440737647137519120,
%U A258422 2601107886874207253760,89332305977055996111040,2995343867463073686769440,98555316817167057069129600
%N A258422 Number of partitions of the 8-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 A258422 Alois P. Heinz, <a href="/A258422/b258422.txt">Table of n, a(n) for n = 8..650</a>
%p A258422 b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
%p A258422        A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
%p A258422     end:
%p A258422 A:= proc(n, k) option remember; `if`(n=0, 1,
%p A258422       -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
%p A258422     end:
%p A258422 T:= proc(n, k) option remember;
%p A258422       add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
%p A258422     end:
%p A258422 a:= n-> T(n, 8):
%p A258422 seq(a(n), n=8..25);
%Y A258422 Column k=8 of A255982.
%K A258422 nonn
%O A258422 8,1
%A A258422 _Alois P. Heinz_, May 29 2015