[seqfan] k-Minumums of a Permutation

[Ron Hardin]

Each row apparently eventually reaches super-Catalan numbers A001003

T(n,k)=Number of n element 1..n arrays with each element the minimum of k 
adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements

Table starts
.........1.........1........1........1.......1......1......1......1.....1....1
.........2.........3........3........3.......3......3......3......3.....3....3
.........6........10.......11.......11......11.....11.....11.....11....11...11
........24........40.......44.......45......45.....45.....45.....45....45...45
.......120.......182......192......196.....197....197....197....197...197..197
.......720.......938......892......898.....902....903....903....903...903..903
......5040......5424.....4400.....4272....4274...4278...4279...4279..4279.4279
.....40320.....34788....23086....21002...20790..20788..20792..20793.20793.....
....362880....244544...129250...106564..103354.103050.103044.103048...........
...3628800...1865144...773868...558780..523786.519268.518864..................
..39916800..15312976..4953208..3037926.2703206................................
.479001600.134495328.33778104.17203726........................................


 rhhardin at mindspring.com
rhhardin at att.net (either)