Triangle T(n,k) giving number of Dyck paths of length 2n with exactly k hills (0 <= k <= n).

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =0a(5) =1a(6) =2a(7) =2a(8) =0a(9) =1a(10) =6a(11) =4a(12) =3a(13) =0a(14) =1a(15) =18a(16) =13a(17) =6a(18) =4a(19) =0a(20) =1a(21) =57a(22) =40a(23) =21a(24) =8a(25) =5a(26) =0a(27) =1a(28) =186a(29) =130