|
Search: id:A123922
|
|
|
| A123922 |
|
Number of 2143-avoiding Dumont paths of the 2nd kind of length 2n. |
|
+0
1
|
|
| 1, 1, 2, 6, 21, 84, 360, 1650, 7865, 39039, 198744, 1039584, 5534928, 30046752, 165257136, 922280634, 5199131025, 29644168125, 170375955750, 988180543350, 5768664340725, 33927954699600, 200617471267200, 1193673954039840
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
A. Burstein, S. Elizalde and T. Mansour, Restricted Dumond Permutations, Dyck Paths and Noncrossing Partitions.
|
|
FORMULA
|
a(n)=A047749(n)*A047749(n+1).
|
|
EXAMPLE
|
For n=2, there are 3 Dumont permutations of the 2nd kind of length 2n=4, namely {2143,3142,4132}.
Avoiding 2143, the cardinality of this set is reduced to a(2)=2.
|
|
PROGRAM
|
(PARI) A047749(n)={ local(m) ; m=floor(n/2) ; if(n %2, return(binomial(3*m+1, m+1)/(2*m+1)), return(binomial(3*m, m)/(2*m+1)) ) ; } a(n)={ return(A047749(n)*A047749(n+1)) ; } { for(n=0, 25, print1(a(n), ", ") ; ) ; }
|
|
CROSSREFS
|
Cf. A001469, A047749.
Sequence in context: A063689 A058866 A087649 this_sequence A099947 A121726 A090805
Adjacent sequences: A123919 A123920 A123921 this_sequence A123923 A123924 A123925
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 20 2006
|
|
|
Search completed in 0.002 seconds
|
