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A275514 Triangle read by rows: the coefficient [t^k] of the Ehrhart polynomial of the 2-hypersimplex in dimension n. 1
1, 1, -1, 1, 0, 0, 1, 2, 1, 0, 1, 5, 5, 0, 0, 1, 9, 15, 1, 0, 0, 1, 14, 35, 7, 0, 0, 0, 1, 20, 70, 28, 1, 0, 0, 0, 1, 27, 126, 84, 9, 0, 0, 0, 0, 1, 35, 210, 210, 45, 1, 0, 0, 0, 0, 1, 44, 330, 462, 165, 11, 0, 0, 0, 0, 0, 1, 54, 495, 924, 495, 66, 1, 0, 0, 0, 0, 0, 1, 65, 715 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Table of n, a(n) for n=1..81.

Nan Li, Ehrhart h*-vectors of hypersimplices, Discr. Comp. Geom. 48 (2012) 847-878, Eq. (1.1)

EXAMPLE

The triangle starts in row n=1 with coefficients 0<=k<n as:

1;

1, -1;

1, 0, 0;

1, 2, 1, 0;

1, 5, 5, 0, 0;

1, 9, 15, 1, 0, 0;

1, 14, 35, 7, 0, 0, 0;

1, 20, 70, 28, 1, 0, 0, 0;

1, 27, 126, 84, 9, 0, 0, 0, 0;

1, 35, 210, 210, 45, 1, 0, 0, 0, 0;

1, 44, 330, 462, 165, 11, 0, 0, 0, 0, 0;

1, 54, 495, 924, 495, 66, 1, 0, 0, 0, 0, 0;

1, 65, 715, 1716, 1287, 286, 13, 0, 0, 0, 0, 0, 0;

MAPLE

subki := proc(n, r, l)

    local i, t;

    add(t^i, i=0..l-1) ;

    %^n ;

    expand(%) ;

    coeff(%, t, r) ;

end proc:

hstard := proc(d, k, n)

    add((-1)^i*binomial(n, i)*subki(n, (k-i)*d-i, k-i) , i=0..k-1) ;

end proc:

A275514 := proc(n, k)

    hstard(k, 2, n)

end proc:

CROSSREFS

Cf. A010054 (coefficients for the 1-hypersimplex), A258993, A000295 (row sums), A000096 (column k=1), A000332 (k=2), A000579 (k=3), A000581 (k=4), A001287 (k=5).

Sequence in context: A239145 A327127 A151824 * A180782 A213597 A302978

Adjacent sequences:  A275511 A275512 A275513 * A275515 A275516 A275517

KEYWORD

sign,tabl,easy

AUTHOR

R. J. Mathar, Jul 31 2016

STATUS

approved

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Last modified July 6 02:58 EDT 2022. Contains 355108 sequences. (Running on oeis4.)