Triangle read by rows, T(n,k) for 0<=k<=n, generalizes the colored Motzkin paths of A107264.

Terms

a(0) =1a(1) =3a(2) =1a(3) =12a(4) =6a(5) =1a(6) =54a(7) =33a(8) =9a(9) =1a(10) =261a(11) =180a(12) =63a(13) =12a(14) =1a(15) =1323a(16) =990a(17) =405a(18) =102a(19) =15a(20) =1a(21) =6939a(22) =5508a(23) =2511a(24) =756a(25) =150a(26) =18a(27) =1a(28) =37341a(29) =30996