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A076756
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Triangle of coefficients of characteristic polynomial of M_n, the n X n matrix M_(i,j) = min(i,j).
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7
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1, -1, 1, 1, -3, 1, -1, 5, -6, 1, 1, -7, 15, -10, 1, -1, 9, -28, 35, -15, 1, 1, -11, 45, -84, 70, -21, 1, -1, 13, -66, 165, -210, 126, -28, 1, 1, -15, 91, -286, 495, -462, 210, -36, 1, -1, 17, -120, 455, -1001, 1287, -924, 330, -45, 1, 1, -19, 153, -680, 1820, -3003, 3003, -1716, 495, -55, 1
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OFFSET
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0,5
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COMMENTS
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The characteristic polynomial of M_n seems to be p(n,x) = (-1)^n * sum_{i=0..n} (-x)^i * binomial(2n-i, i). - Enrique Pérez Herrero, Jan 29 2013
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LINKS
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EXAMPLE
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Triangle begins:
1;
-1, 1;
1, -3, 1;
-1, 5, -6, 1;
1, -7, 15, -10, 1;
-1, 9, -28, 35, -15, 1;
1, -11, 45, -84, 70, -21, 1;
-1, 13, -66, 165, -210, 126, -28, 1;
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MAPLE
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T:=(n, k)-> binomial(2*n-k, k)*(-1)^(n+k):
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MATHEMATICA
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T[n_, k_] := Binomial[2*n - k, k]*(-1)^(n + k); Table[Table[T[n, k], {k, 0, n}], {n, 0, 14}] // Flatten (* Jean-François Alcover, Jun 12 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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