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A158193
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A triangle sequence from the identity of Matjaz Konvalinka: t(n,m)=Sum[(-1)^m*Binomial[n, i - m]*Binomial[n, i]*Binomial[n, i + m], {i, m, n - m}]/2.
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0
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-1, -9, -72, 3, -550, 50, -4140, 585, -10, -31017, 5880, -245, -232288, 54488, -3808, 35, -1742148, 480816, -47880, 1134, -13095450, 4110750, -532350, 22050, -126, -98687600, 34397880, -5466780, 333960, -5082, -745652160, 283510260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Row sums are:
{-1, -9, -69, -500, -3565, -25382, -181573, -1308078, -9495126, -69427622,
-511055061,...}.
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LINKS
| Matjaz Konvalinka, An inverse matrix formula in the right-quantum algebra, Electron. J. Combin. 15 (2008), R23.
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FORMULA
| t(n,m)=Sum[(-1)^m*Binomial[n, i - m]*Binomial[n, i]*Binomial[n, i + m], {i, m, n - m}]/2.
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EXAMPLE
| {-1},
{-9},
{-72, 3},
{-550, 50},
{-4140, 585, -10},
{-31017, 5880, -245},
{-232288, 54488, -3808, 35},
{-1742148, 480816, -47880, 1134},
{-13095450, 4110750, -532350, 22050, -126},
{-98687600, 34397880, -5466780, 333960, -5082},
{-745652160, 283510260, -53143200, 4348377, -118800, 462}
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MATHEMATICA
| Table[Table[ Sum[(-1)^m* Binomial[n, i - m]*Binomial[n, i]*Binomial[n, i + m], {i, m, n - m}]/2, {m, 1, Floor[n/2]}], {n, 2, 12}];
Flatten[%]
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CROSSREFS
| Sequence in context: A178869 A057080 A001706 * A123987 A003365 A044196
Adjacent sequences: A158190 A158191 A158192 * A158194 A158195 A158196
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KEYWORD
| sign,tabf,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2009
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