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A158854
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Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial (1-x)^(1+floor(n/2))* (1+x)^floor((n-1)/2) in row n, column k.
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3
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1, 1, -1, 1, -2, 1, 1, -1, -1, 1, 1, -2, 0, 2, -1, 1, -1, -2, 2, 1, -1, 1, -2, -1, 4, -1, -2, 1, 1, -1, -3, 3, 3, -3, -1, 1, 1, -2, -2, 6, 0, -6, 2, 2, -1, 1, -1, -4, 4, 6, -6, -4, 4, 1, -1, 1, -2, -3, 8, 2, -12, 2, 8, -3, -2, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are zero except for n=0.
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LINKS
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FORMULA
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T(n,k) = T(n-2,k) - T(n-2,k-2), T(0,0) = T(1,0) = T(2,0) = T(2,2) = 1, T(1,1)=-1, T(2,1)=-2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Oct 25 2013
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EXAMPLE
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1;
1, -1;
1, -2, 1;
1, -1, -1, 1;
1, -2, 0, 2, -1;
1, -1, -2, 2, 1, -1;
1, -2, -1, 4, -1, -2, 1;
1, -1, -3, 3, 3, -3, -1, 1;
1, -2, -2, 6, 0, -6, 2, 2, -1;
1, -1, -4, 4, 6, -6, -4, 4, 1, -1;
1, -2, -3, 8, 2, -12, 2, 8, -3, -2, 1;
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MAPLE
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(1-x)^(1+floor(n/2))*(1+x)^floor((n-1)/2) ;
coeftayl(%, x=0, k) ;
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MATHEMATICA
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Clear[p, x, n, m, a];
p[x_, n_] = If[n == 0, 1, (1 - x)^(Floor[(n)/ 2] + 1)(1 + x)^(Floor[(n - 1)/2])];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
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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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