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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
OFFSET
1,8
LINKS
Robert Coquereaux and Jean-Bernard Zuber, Counting partitions by genus. II. A compendium of results, arXiv:2305.01100 [math.CO], 2023. See p. 10.
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
KEYWORD
sign,tabl,easy
AUTHOR
R. J. Mathar, Jul 31 2016
STATUS
approved