Triangle read by rows: T(n,k) is the number of hill-free Dyck paths of semilength n and having k UUDD's, where U=(1,1) and D=(1,-1) (0<=k<=floor(n/2), n>=2). A hill in a Dyck path is a peak at level 1.

A105640

Triangle read by rows: T(n,k) is the number of hill-free Dyck paths of semilength n and having k UUDD's, where U=(1,1) and D=(1,-1) (0<=k<=floor(n/2), n>=2). A hill in a Dyck path is a peak at level 1.