|
Search: id:A152887
|
|
|
| A152887 |
|
Number of descents beginning with an even number and ending with an odd number in all permutations of {1,2,...,n}. |
|
+0
3
|
|
| 0, 1, 2, 18, 72, 720, 4320, 50400, 403200, 5443200, 54432000, 838252800, 10059033600, 174356582400, 2440992153600, 47076277248000, 753220435968000, 16005934264320000, 288106816757760000, 6690480522485760000
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
FORMULA
|
a(2n)=(2n-1)*binom(n+1,2); a(2n+1)=(2n)!*binom(n+1,2).
|
|
EXAMPLE
|
a(8)=50400 because (i) the descent pairs can be chosen in 1+2+3+4=10 ways, namely (2,1),(4,1),(4,3),(6,1),(6,3),(6,5),(8,1),(8,3),(8,5),(8,7); (ii) they can be placed in 7 positions, namely (1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8); (iii) the remaining 6 entries can be permuted in 6!=720 ways; 10*7*720=50400.
|
|
MAPLE
|
a := proc (n) if `mod`(n, 2) = 0 then factorial(n-1)*binomial((1/2)*n+1, 2) else factorial(n-1)*binomial((1/2)*n+1/2, 2) end if end proc: seq(a(n), n = 1 .. 22);
|
|
CROSSREFS
|
A152885, A152886
Sequence in context: A073976 A120361 A120358 this_sequence A098817 A034473 A024171
Adjacent sequences: A152884 A152885 A152886 this_sequence A152888 A152889 A152890
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 19 2009
|
|
|
Search completed in 0.002 seconds
|
