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A174160
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A symmetrical triangular sequence:t(n,m)=2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2
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0
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1, 1, 1, 1, -1, 1, 1, -14, -14, 1, 1, -48, -268, -48, 1, 1, -111, -1896, -1896, -111, 1, 1, -201, -8643, -25793, -8643, -201, 1, 1, -290, -29830, -208862, -208862, -29830, -290, 1, 1, -292, -83680, -1206508, -2799316, -1206508, -83680, -292, 1, 1, 1
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OFFSET
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1,8
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COMMENTS
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Row sums are:
{1, 2, 1, -26, -362, -4012, -43479, -477962, -5380274, -62040980,...}.
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LINKS
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FORMULA
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t(n,m)=2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2
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EXAMPLE
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{1},
{1, 1},
{1, -1, 1},
{1, -14, -14, 1},
{1, -48, -268, -48, 1},
{1, -111, -1896, -1896, -111, 1},
{1, -201, -8643, -25793, -8643, -201, 1},
{1, -290, -29830, -208862, -208862, -29830, -290, 1},
{1, -292, -83680, -1206508, -2799316, -1206508, -83680, -292, 1},
{1, 1, -195920, -5440016, -25384556, -25384556, -5440016, -195920, 1, 1}
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MATHEMATICA
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<< DiscreteMath`Combinatorica`
t[n_, m_] =2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2;
Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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