Triangle read by rows: T(n,k) = binomial(3n+3, k)*(n-k+1)/(n+1).

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =6a(5) =12a(6) =1a(7) =9a(8) =33a(9) =55a(10) =1a(11) =12a(12) =63a(13) =182a(14) =273a(15) =1a(16) =15a(17) =102a(18) =408a(19) =1020a(20) =1428a(21) =1a(22) =18a(23) =150a(24) =760a(25) =2565a(26) =5814a(27) =7752a(28) =1a(29) =21