%I A071223
%S A071223 2,2,6,2,12,24,2,20,72,120,2,30,172,480,720,2,42,352,1512,3600,5040,2,
%T A071223 56,646,3976,14184,30240,40320,2,72,1094,9144,45992,143712,282240,
%U A071223 362880,2,90,1742,18990,128288,557640,1575648,2903040,3628800,2,110
%N A071223 Triangle T(n,k) (n >= 2, 1 <= k <= n) read by rows: number of linearly 
               inducible orderings of n points in k-dimensional Euclidean space.
%D A071223 T. M. Cover, The number of linearly inducible orderings of points in 
               d-space, SIAM J. Applied Math., 15 (1967), 434-439.
%F A071223 T(n, 1)=2 for n>=2, T(2, k)=2 for k>=1, T(n+1, k) = T(n, k)+n*T(n, k-1). 
               Also T(n, k) = n! for k >= n-1.
%e A071223 Triangle begins:
%e A071223 2
%e A071223 2 6
%e A071223 2 12 24
%e A071223 2 20 72 120
%e A071223 2 30 172 480 720
%p A071223 T:=proc(n,k) if k>=n then 0 elif k=1 and n>=2 then 2 elif n=2 and k>=1 
               then 2 elif k=n-1 then n! else T(n-1,k)+(n-1)*T(n-1,k-1) fi end:seq(seq(T(n,
               k),k=1..n-1),n=2..12);
%Y A071223 Cf. A087644. Second and third columns = A002378, A087645.
%Y A071223 Sequence in context: A099985 A110765 A091818 this_sequence A055934 A096217 
               A098555
%Y A071223 Adjacent sequences: A071220 A071221 A071222 this_sequence A071224 A071225 
               A071226
%K A071223 nonn,tabl,easy,nice
%O A071223 2,1
%A A071223 N. J. A. Sloane (njas(AT)research.att.com), Oct 26 2003
%E A071223 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 24 2004