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A141901
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A skew triangle sequence of coefficients: t(n,m)=If[n*m == 0, 1, (n *Gamma[n] *Hypergeometric2F1[1, 1 + m - n, 2 + m, -1])/(Gamma[2 + m]* Gamma[ -m + n]) - 2^(n - m)].
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0
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1, 1, -1, 1, -1, -1, 1, 0, -1, -1, 1, 3, 1, -1, -1, 1, 10, 8, 2, -1, -1, 1, 25, 26, 14, 3, -1, -1, 1, 56, 67, 48, 21, 4, -1, -1, 1, 119, 155, 131, 77, 29, 5, -1, -1, 1, 246, 338, 318, 224, 114, 38, 6, -1, -1, 1, 501, 712, 720, 574, 354, 160, 48, 7, -1, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Row sums are:
{1, 0, -1, -1, 3, 19, 67, 195, 515, 1283, 3075}.
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FORMULA
| t(n,m)=If[n*m == 0, 1, (n *Gamma[n] *Hypergeometric2F1[1, 1 + m - n, 2 + m, -1])/(Gamma[2 + m]* Gamma[ -m + n]) - 2^(n - m)].
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EXAMPLE
| {1},
{1, -1},
{1, -1, -1},
{1, 0, -1, -1},
{1, 3, 1, -1, -1},
{1, 10, 8, 2, -1, -1},
{1, 25, 26, 14, 3, -1, -1},
{1, 56, 67, 48, 21, 4, -1, -1},
{1, 119, 155, 131, 77, 29, 5, -1, -1},
{1, 246, 338, 318, 224, 114, 38,6, -1, -1},
{1, 501, 712, 720, 574, 354, 160, 48, 7, -1, -1}
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MATHEMATICA
| t[n_, m_] = If[n*m == 0, 1, (n *Gamma[n] *Hypergeometric2F1[1, 1 + m - n, 2 + m, -1])/(Gamma[2 + m]* Gamma[ -m + n]) - 2^(n - m)]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A119329 A054724 A061494 * A200473 A180172 A090751
Adjacent sequences: A141898 A141899 A141900 * A141902 A141903 A141904
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 13 2008
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