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Search: id:A145889
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| A145889 |
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Number of even entries that are followed by a smaller entry in all permutations of {1,2,...,n}. |
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+0
1
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| 0, 1, 2, 24, 96, 1080, 6480, 80640, 645120, 9072000, 90720000, 1437004800, 17244057600, 305124019200, 4271736268800, 83691159552000, 1339058552832000, 28810681675776000, 518592270163968000, 12164510040883200000
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A134434(n,k),k=0..floor(n/2)).
The average of the number of even entries that start a descent over all permutations of {1,2,...n} is (1/n)[floor(n/2)]^2.
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REFERENCES
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S. Kitaev and J. Remmel, Classifying descents according to parity, Annals of Combinatorics, 11, 2007, 173-193.
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FORMULA
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a(2n)=n(2n)!/2; a(2n+1)=n^2*(2n)!.
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EXAMPLE
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a(3)=2 because the permutations of {1,2,3} are 123, 132, 2'13, 231, 312 and 32'1 with the even entries that start a descent marked.
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MAPLE
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a:=proc(n) if `mod`(n, 2)=0 then (1/4)*n*factorial(n) else (1/4)*(n-1)^2*factorial(n-1) end if end proc: seq(a(n), n=1..20);
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CROSSREFS
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A134434, A145890
Sequence in context: A136280 A123831 A138648 this_sequence A121199 A009538 A009556
Adjacent sequences: A145886 A145887 A145888 this_sequence A145890 A145891 A145892
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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), Nov 16 2008
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