|
| |
|
|
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; 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.
|
|
|
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
| A134434, A145890
Sequence in context: A123831 A138648 A172225 * A121199 A009538 A009556
Adjacent sequences: A145886 A145887 A145888 * A145890 A145891 A145892
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2008
|
| |
|
|
