A304635 Triangle T(n,j) read by rows: the number of j-faces in the hypersimplicial decomposition of the unit cube of n dimensions.

1, 5, 2, 18, 14, 3, 56, 64, 27, 4, 160, 240, 150, 44, 5, 432, 800, 660, 288, 65, 6, 1120, 2464, 2520, 1456, 490, 90, 7, 2816, 7168, 8736, 6272, 2800, 768, 119, 8, 6912, 19968, 28224, 24192, 13440, 4896, 1134, 152, 9, 16640, 53760, 86400, 86016, 57120, 25920, 7980, 1600, 189, 10

Offset: 1

Author

R. J. Mathar, May 15 2018

Keywords

• nonn
• tabl
• easy

Examples

			The triangle starts in row n>= for 1<=j<=n as:
  1,
5,2,
18,14,3,
56,64,27,4,
160,240,150,44,5,
432,800,660,288,65,6,
1120,2464,2520,1456,490,90,7,
2816,7168,8736,6272,2800,768,119,8,
6912,19968,28224,24192,13440,4896,1134,152,9,
16640,53760,86400,86016,57120,25920,7980,1600,189,10,
		

Links

• T. Hibi, N. Li, H. Ohsugi, The Face Vector of a Half-Open Hypersimplex, J. Int. Seq. 18 (2015) 15.6.6

Crossrefs

Cf. A001793 (column j=1), A001794 (half of column j=2), A006974 (3rd of column j=3), A014106 (subdiagonal).

Programs

Maple

A304635 := proc(n,j)
        j*2^(n-j-1)*(n+j+2)/(n+1)*binomial(n+1,j+1) ;
end proc:

Formula

T(n,j) = j*2^(n-j-1)*(n+j+2)*binomial(n+,j+1)/(n+1).