|
| |
|
|
A056986
|
|
Number of permutations on {1,...,n} containing any given pattern alpha in the symmetric group S_3.
|
|
121
| |
|
|
0, 0, 1, 10, 78, 588, 4611, 38890, 358018, 3612004, 39858014, 478793588, 6226277900, 87175616760, 1307664673155, 20922754530330, 355687298451210, 6402373228089300, 121645098641568810, 2432902001612519580
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| This is well-defined because for all patterns alpha in S_3 the number of permutations in S_n avoiding alpha is the same (the Catalan numbers). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2008
|
|
|
REFERENCES
| R. Simion and F.W. Schmidt, Restricted Permutations, Europ. J. Comb., 6, 1985, 383-406.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Permutation Pattern
|
|
|
EXAMPLE
| a(4)=10 because, taking, for example, the pattern alpha=321, we have 3214, 3241, 1432, 2431, 3421, 4213, 4132, 4231, 4312 and 4321.
|
|
|
MATHEMATICA
| n!-Binomial[2n, n]/(n+1)
|
|
|
PROG
| (PARI) a(n)=n!-binomial(n+n, n+1)/n \\ Charles R Greathouse IV, Jun 10 2011
|
|
|
CROSSREFS
| Sequence in context: A080618 A082136 A153596 * A160655 A006469 A081905
Adjacent sequences: A056983 A056984 A056985 * A056987 A056988 A056989
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
| |
|
|
