Triangle read by rows: T(n,k) = the number of Dyck paths of semilength n with k DUUU's.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =1a(6) =35a(7) =7a(8) =96a(9) =36a(10) =267a(11) =159a(12) =3a(13) =750a(14) =645a(15) =35a(16) =2123a(17) =2475a(18) =264a(19) =6046a(20) =9136a(21) =1602a(22) =12a(23) =17303a(24) =32773a(25) =8515a(26) =195a(27) =49721a(28) =115017a(29) =41349