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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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

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

FORMULA

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

EXAMPLE

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,

MAPLE

A304635 := proc(n, j)

        j*2^(n-j-1)*(n+j+2)/(n+1)*binomial(n+1, j+1) ;

end proc:

CROSSREFS

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

Sequence in context: A286161 A286252 A286154 * A306198 A276533 A303685

Adjacent sequences:  A304632 A304633 A304634 * A304636 A304637 A304638

KEYWORD

nonn,tabl,easy

AUTHOR

R. J. Mathar, May 15 2018

STATUS

approved

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Last modified September 19 15:08 EDT 2019. Contains 327198 sequences. (Running on oeis4.)