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Search: id:A142070
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| A142070 |
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A triangle of coefficients of rational root polynomials: p(x,n)=Product[(i + 1)*x - i, {i, 1, n}]. |
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+0
1
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| 1, -1, 2, 2, -7, 6, -6, 29, -46, 24, 24, -146, 329, -326, 120, -120, 874, -2521, 3604, -2556, 720, 720, -6084, 21244, -39271, 40564, -22212, 5040, -5040, 48348, -197380, 444849, -598116, 479996, -212976, 40320, 40320, -432144, 2014172, -5335212, 8788569, -9223012, 6023772, -2239344, 362880
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are one.
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FORMULA
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p(x,n)=Product[(i + 1)*x - i, {i, 1, n}]; t(n,m)=Coefficients(p(x,n)).
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EXAMPLE
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{1},
{-1, 2},
{2, -7, 6},
{-6, 29, -46, 24},
{24, -146, 329, -326, 120},
{-120, 874, -2521, 3604, -2556, 720},
{720, -6084, 21244, -39271, 40564, -22212, 5040},
{-5040,48348, -197380, 444849, -598116, 479996, -212976, 40320},
{40320, -432144, 2014172, -5335212,8788569, -9223012, 6023772, -2239344, 362880},
{-362880, 4292496, -22448988, 68158628, -132449241, 170892798, -146444068,80391816, -25659360, 3628800},
{3628800, -46916640, 271707336, -928525148, 2074237318, -3165869631, 3344261458, -2414802908, 1140903576, -318540960, 39916800}
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MATHEMATICA
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Clear[p, x, n, m]; p[x_, n_] := Product[(i + 1)*x - i, {i, 1, n}]; Table[Expand[p[x, n]], {n, 0, 10}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A006748 A131049 A126851 this_sequence A152825 A064288 A054085
Adjacent sequences: A142067 A142068 A142069 this_sequence A142071 A142072 A142073
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 15 2008
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