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A360205
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Triangle read by rows. T(n, k) = (-1)^(n-k)*(k+1)*binomial(n, k)*pochhammer(1-n, n-k).
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2
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1, 0, 2, 0, 4, 3, 0, 12, 18, 4, 0, 48, 108, 48, 5, 0, 240, 720, 480, 100, 6, 0, 1440, 5400, 4800, 1500, 180, 7, 0, 10080, 45360, 50400, 21000, 3780, 294, 8, 0, 80640, 423360, 564480, 294000, 70560, 8232, 448, 9, 0, 725760, 4354560, 6773760, 4233600, 1270080, 197568, 16128, 648, 10
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OFFSET
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0,3
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COMMENTS
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A refinement of the number of partial permutations of an n-set (A002720).
Also the coefficients of a shifted derivative of the unsigned Lah polynomials (A271703).
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LINKS
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EXAMPLE
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Triangle T(n, k) starts:
[0] 1;
[1] 0, 2;
[2] 0, 4, 3;
[3] 0, 12, 18, 4;
[4] 0, 48, 108, 48, 5;
[5] 0, 240, 720, 480, 100, 6;
[6] 0, 1440, 5400, 4800, 1500, 180, 7;
[7] 0, 10080, 45360, 50400, 21000, 3780, 294, 8;
[8] 0, 80640, 423360, 564480, 294000, 70560, 8232, 448, 9;
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MAPLE
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T := (n, k) -> (-1)^(n - k)*(k + 1)*binomial(n, k)*pochhammer(1 - n, n - k):
seq(seq(T(n, k), k = 0..n), n = 0..9);
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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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