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A136449
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Hankel matrices are antidiagonals with decreasing n from the middle antidiagonal: here the characteristic polynomials of the matrices are made into a triangle of coefficients.
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0
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1, 1, -1, -4, -1, 1, -27, 10, 4, -1, 256, 43, -42, -4, 1, 3125, -686, -398, 72, 9, -1, -46656, -5885, 5774, 542, -180, -9, 1, -823543, 127282, 86112, -11640, -2460, 264, 16, -1, 16777216, 1692439, -1666738, -138336, 51576, 3100, -520, -16, 1, 387420489, -46044262, -33920458, 3633796, 967479, -88890
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OFFSET
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1,4
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COMMENTS
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Row sums are:
1, 0, -4, -14, 254, 2121, -46413, -623970, 16718722, 311959028, -9975349928
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REFERENCES
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C. Brezinski, Biorthogonal Polynomials And The Bordering Method For Linear Systems (1993):http://citeseer.ist.psu.edu/brezinski93biorthogonal.html
Weisstein, Eric W. "Hankel Matrix." http://mathworld.wolfram.com/HankelMatrix.html
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LINKS
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Table of n, a(n) for n=1..51.
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FORMULA
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Matrices are h(i,j) = If[i + j - 1 > n, 0, i + j - 1] for i,j < =n.
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EXAMPLE
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{1},
{1, -1},
{-4, -1, 1},
{-27, 10,4, -1},
{256, 43, -42, -4, 1},
{3125, -686, -398, 72, 9, -1},
{-46656, -5885, 5774, 542, -180, -9, 1},
{-823543, 127282, 86112, -11640, -2460, 264, 16, -1},
{16777216, 1692439, -1666738, -138336, 51576, 3100, -520, -16, 1},
{387420489, -46044262, -33920458, 3633796, 967479, -88890, -9850, 700, 25, -1},
{-10000000000, -840097729, 829514502, 60334298, -23981636, -1413279, 283290, 11850, -1200, -25, 1}
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MATHEMATICA
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H[n_] := Table[Table[If[i + j - 1 > n, 0, i + j - 1], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]]; Flatten[a]
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CROSSREFS
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Cf. A000312.
Sequence in context: A220652 A169654 A088158 * A209427 A140805 A113370
Adjacent sequences: A136446 A136447 A136448 * A136450 A136451 A136452
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula, Mar 19 2008
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STATUS
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approved
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