Triangle of Dyck paths counted by number of long interior inclines.

Terms

a(0) =2a(1) =3a(2) =2a(3) =4a(4) =8a(5) =2a(6) =5a(7) =20a(8) =15a(9) =2a(10) =6a(11) =40a(12) =60a(13) =24a(14) =2a(15) =7a(16) =70a(17) =175a(18) =140a(19) =35a(20) =2a(21) =8a(22) =112a(23) =420a(24) =560a(25) =280a(26) =48a(27) =2a(28) =9a(29) =168