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%I #7 May 15 2018 17:06:02
%S 1,5,2,18,14,3,56,64,27,4,160,240,150,44,5,432,800,660,288,65,6,1120,
%T 2464,2520,1456,490,90,7,2816,7168,8736,6272,2800,768,119,8,6912,
%U 19968,28224,24192,13440,4896,1134,152,9,16640,53760,86400,86016,57120,25920,7980,1600,189,10
%N Triangle T(n,j) read by rows: the number of j-faces in the hypersimplicial decomposition of the unit cube of n dimensions.
%H T. Hibi, N. Li, H. Ohsugi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Li/li41.html">The Face Vector of a Half-Open Hypersimplex</a>, J. Int. Seq. 18 (2015) 15.6.6
%F T(n,j) = j*2^(n-j-1)*(n+j+2)*binomial(n+,j+1)/(n+1).
%e The triangle starts in row n>= for 1<=j<=n as:
%e 1,
%e 5,2,
%e 18,14,3,
%e 56,64,27,4,
%e 160,240,150,44,5,
%e 432,800,660,288,65,6,
%e 1120,2464,2520,1456,490,90,7,
%e 2816,7168,8736,6272,2800,768,119,8,
%e 6912,19968,28224,24192,13440,4896,1134,152,9,
%e 16640,53760,86400,86016,57120,25920,7980,1600,189,10,
%p A304635 := proc(n,j)
%p j*2^(n-j-1)*(n+j+2)/(n+1)*binomial(n+1,j+1) ;
%p end proc:
%Y Cf. A001793 (column j=1), A001794 (half of column j=2), A006974 (3rd of column j=3), A014106 (subdiagonal).
%K nonn,tabl,easy
%O 1,2
%A _R. J. Mathar_, May 15 2018
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