Three-Catalan Triangle read by rows, for n>=0 and k>=0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =4a(6) =9a(7) =11a(8) =10a(9) =6a(10) =3a(11) =1a(12) =34a(13) =90a(14) =120a(15) =120a(16) =96a(17) =64a(18) =35a(19) =15a(20) =5a(21) =1a(22) =364a(23) =1000a(24) =1400a(25) =1505a(26) =1351a(27) =1044a(28) =700a(29) =406