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A358112
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Table read by rows. A statistic of permutations of the multiset {1,1,2,2,...,n,n}.
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0
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1, 5, 1, 47, 42, 1, 641, 1659, 219, 1, 11389, 72572, 28470, 968, 1, 248749, 3610485, 3263402, 357746, 4017, 1, 6439075, 204023334, 371188155, 95559940, 3853617, 16278, 1, 192621953, 12989570167, 43844432805, 22448025251, 2216662051, 38270373, 65399, 1
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OFFSET
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1,2
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COMMENTS
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Table 1, page 12 in Maazouz and Pitman (note a typo in T(2, 0)).
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LINKS
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FORMULA
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T(n, k) = P(n, k+1) - P(n, k), where P(n, x) = (2*n)!*Sum_{k=0..n} Sum_{j=0..n-k} binomial(n, k)*binomial(n-k, j)*(-1)^(n-k-j)*max(x - k, 0)^(2*n - j)/(2*n - j)!.
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EXAMPLE
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[n\d] 0 1 2 3 4 5 6
-----------------------------------------------------------------------------
[1] 1;
[2] 5, 1;
[3] 47, 42, 1;
[4] 641, 1659, 219, 1;
[5] 11389, 72572, 28470, 968, 1;
[6] 248749, 3610485, 3263402, 357746, 4017, 1;
[7] 6439075, 204023334, 371188155, 95559940, 3853617, 16278, 1
[8] 192621953, 12989570167, 43844432805, 22448025251, 2216662051, 38270373,
65399, 1
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MAPLE
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P := (n, x) -> (2*n)!*add(add(binomial(n, k)*binomial(n-k, j)*
(-1)^(n-k-j)*max(x - k, 0)^(2*n - j)/(2*n - j)!, j = 0..n-k), k = 0..n):
Trow := n -> seq(P(n, k+1) - P(n, k), k = 0..n-1):
seq(print(Trow(n)), n = 1..8);
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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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