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A141690
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Triangle t(n,m) = 2*A008292(n+1,m+1) - A007318(n,m), a linear combination of Eulerian numbers and Pascal's triangle, 0 <= m <= n.
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2
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1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 48, 126, 48, 1, 1, 109, 594, 594, 109, 1, 1, 234, 2367, 4812, 2367, 234, 1, 1, 487, 8565, 31203, 31203, 8565, 487, 1, 1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1, 1, 2017, 95644, 910300, 2620582, 2620582, 910300
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OFFSET
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0,5
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COMMENTS
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Row sums are 1, 2, 8, 40, 224, 1408, 10016, 80512, 725504, 7257088, ... = 2*(n+1)! - 2^n.
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LINKS
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 6, 1;
1, 19, 19, 1;
1, 48, 126, 48, 1;
1, 109, 594, 594, 109, 1;
1, 234, 2367, 4812, 2367, 234, 1;
1, 487, 8565, 31203, 31203, 8565, 487, 1;
1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1;
1, 2017, 95644, 910300, 2620582, 2620582, 910300, 95644, 2017, 1;
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MAPLE
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2*A008292(n+1, m+1)-binomial(n, m) ;
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MATHEMATICA
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Table[Table[(2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]), {k, 0, n - 1}], {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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