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A145889 Number of even entries that are followed by a smaller entry in all permutations of {1,2,...,n}. 0
0, 1, 2, 24, 96, 1080, 6480, 80640, 645120, 9072000, 90720000, 1437004800, 17244057600, 305124019200, 4271736268800, 83691159552000, 1339058552832000, 28810681675776000, 518592270163968000, 12164510040883200000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

REFERENCES

S. Kitaev and J. Remmel, Classifying descents according to parity, Annals of Combinatorics, 11, 2007, 173-193.

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(2n) = n(2n)!/2; a(2n+1) = n^2*(2n)!.

EXAMPLE

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.

MAPLE

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);

CROSSREFS

Cf. A134434, A145890.

Sequence in context: A123831 A138648 A172225 * A212568 A121199 A009538

Adjacent sequences:  A145886 A145887 A145888 * A145890 A145891 A145892

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 16 2008

STATUS

approved

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Last modified January 17 16:53 EST 2019. Contains 319235 sequences. (Running on oeis4.)