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A275514
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Triangle read by rows: the coefficient [t^k] of the Ehrhart polynomial of the 2-hypersimplex in dimension n.
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1
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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
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graph;
refs;
listen;
history;
text;
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OFFSET
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1,8
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LINKS
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EXAMPLE
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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;
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MAPLE
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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:
hstard(k, 2, n)
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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