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Search: id:A158194
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| A158194 |
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a(n)=Sum_{i=1..n-1} (-1)^i*binomial(n,i-1)*binomial(n,i)*binomial(n, i+1). |
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+0
1
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| 0, -2, 0, 48, 0, -1080, 0, 24640, 0, -573300, 0, 13571712, 0, -325909584, 0, 7918859520, 0, -194292083700, 0, 4806057828000, 0, -119708452543680, 0, 2999393069557248, 0, -75538616795314400, 0, 1910952839165529600, 0
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Alternating row sums of a symmetric triangle displaying products of three adjacent terms of the Pascal triangle:
2;
9,9;
24,96,24;
50,500,500,50;
90,1800,4500,1800,90;
147,5145,25725,25725,5145,147;
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REFERENCES
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Matjaz Konvalinka, An inverse matrix formula in the right-quantum algebra, Electron. J. Combin., vol. 15 (1) (2008), Article 23.
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LINKS
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Matjaz Konvalinka, An inverse matrix formula in the right-quantum algebra, Electron. J. Combin., vol. 15 (1) (2008), Article 23, Konvalinka home page.
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FORMULA
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a(2m)=2*(-1)^m*binomial(2m,m-1)*binomial(3m,m-1). a(2m-1)=0.
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MATHEMATICA
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Table[Sum[(-1)^i*Binomial[n, i - 1]*Binomial[n, i]*Binomial[n, i + 1], { i, 1, n - 1}], {n, 1, 30}]
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CROSSREFS
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Sequence in context: A145576 A012445 A012450 this_sequence A097173 A009493 A009718
Adjacent sequences: A158191 A158192 A158193 this_sequence A158195 A158196 A158197
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KEYWORD
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sign,easy
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2009
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EXTENSIONS
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Edited by the Associate Editors of the OEIS, Apr 22 2009
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