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Search: id:A136127
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| A136127 |
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Number of permutations of {1,2,...,n} having excedance set {1,2,...,k} for some k=0...n-1 (for k=0 we have the empty set). The excedance set of a permutation p in S_n is the set of indices i such that p(i)>i. |
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2
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| 1, 2, 5, 16, 63, 294, 1585, 9692, 66275, 501106, 4150965, 37383528, 363674407, 3800501438, 42460229945, 505029329524, 6371454458859, 84981113118090, 1194793819467325, 17660505018471680, 273788611235722031
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums of A136126.
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REFERENCES
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R. Ehrenborg and E. Steingrimsson, The excedance set of a permutation, Advances in Appl. Math., 24, 284-299, 2000 (Proposition 6.5).
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FORMULA
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a(n)=Sum(Sum (-1)^(k+1-i)*i!*i^(n-1-k)*Stirling2(k+1,i),i=1..k+1),k=0..n-1).
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EXAMPLE
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a(3)=5 because we have 123,312,213,321, and 231 with excedance sets empty, {1}, {1}, {1}, and {1,2}, respectively.
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MAPLE
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with(combinat): a:=proc(n) options operator, arrow: sum(sum((-1)^(k+1-i)*factorial(i)*i^(n-1-k)*stirling2(k+1, i), i=1..k+1), k=0..n-1) end proc: seq(a(n), n=1..22);
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CROSSREFS
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Cf. A136126.
Adjacent sequences: A136124 A136125 A136126 this_sequence A136128 A136129 A136130
Sequence in context: A124470 A105072 A022494 this_sequence A111004 A079566 A059685
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2008
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