

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
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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, 173193.


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)*(n1)^2*factorial(n1) 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



