Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 3, n-k) for n>=k>=0.

Terms

a(0) =1a(1) =4a(2) =1a(3) =21a(4) =6a(5) =1a(6) =286a(7) =66a(8) =9a(9) =1a(10) =8855a(11) =1540a(12) =171a(13) =13a(14) =1a(15) =501942a(16) =66045a(17) =5984a(18) =378a(19) =18a(20) =1a(21) =45057474a(22) =4582116a(23) =341055a(24) =18424a(25) =741a(26) =24a(27) =1a(28) =5843355957a(29) =470155077