|
|
|
|
| A114494
|
|
Triangle read by rows: T(n,k) is number of hill-free Dyck paths of semilength n and having k returns to the x-axis. (A Dyck path is said to be hill-free if it has no peaks at level 1.)
(history;
published version)
|
|
|
|
|
#26 by Charles R Greathouse IV at Thu Sep 08 08:45:23 EDT 2022
|
|
| PROG
|
(MAGMAMagma) /* except 0 as triangle */ [[(k/(n-k))*Binomial(2*n-2*k, n-2*k): k in [1..n div 2]]: n in [2.. 15]]; // Vincenzo Librandi, Sep 15 2018 *)
|
|
|
|
|
Discussion
|
| Thu Sep 08
| 08:45
| OEIS Server: https://oeis.org/edit/global/2944
|
|
|
|
|
|
|
#25 by Peter Luschny at Sun Sep 16 16:55:39 EDT 2018
|
|
|
|
|
|
|
|
#24 by Joerg Arndt at Sun Sep 16 05:01:57 EDT 2018
|
|
|
|
|
|
|
|
#23 by Jon E. Schoenfield at Sat Sep 15 13:59:46 EDT 2018
|
|
|
|
|
|
|
|
#22 by Jon E. Schoenfield at Sat Sep 15 13:59:43 EDT 2018
|
|
| NAME
|
Triangle read by rows: T(n,k) is number of hill-free Dyck paths of semilength n and having k returns to the x-axis. (A Dyck path is said to be hill-free if it has no peaks at level 1)..)
|
|
| STATUS
|
reviewed
editing
|
|
|
|
|
|
|
#21 by Michel Marcus at Sat Sep 15 09:04:53 EDT 2018
|
|
|
|
|
|
|
|
#20 by Vincenzo Librandi at Sat Sep 15 02:25:05 EDT 2018
|
|
|
|
|
|
|
|
#19 by Vincenzo Librandi at Sat Sep 15 02:24:51 EDT 2018
|
|
| FORMULA
|
T(n, k) = (k/(n-k))*binomial(2n2*n-2k2*k, n-2k2*k) (1 <= k <= floor(n/2)).
|
|
| MATHEMATICA
|
Join[{0}, t[n_, k_]:=(k/(n - k)) Binomial [2 n - 2 k, n - 2 k]; Table[t[n, k], {n, 1, 20}, {k, n/2}]//Flatten] (* Vincenzo Librandi, Sep 15 2018 *)
|
|
| PROG
|
(MAGMA) /* except 0 as triangle */ [[(k/(n-k))*Binomial(2*n-2*k, n-2*k): k in [1..n div 2]]: n in [2.. 15]]; // Vincenzo Librandi, Sep 15 2018 *)
|
|
| STATUS
|
reviewed
editing
|
|
|
|
|
|
|
#18 by Joerg Arndt at Sat Sep 15 02:00:08 EDT 2018
|
|
|
|
|
|
|
|
#17 by Michel Marcus at Sat Sep 15 01:48:37 EDT 2018
|
|
|
|
|
|
|
