Triangle T(n, k) = coefficients of (n+1)!*(binomial(x+n+1, n+1) - binomial(x, n+1)), read by rows.

Terms

a(0) =1a(1) =2a(2) =4a(3) =6a(4) =9a(5) =9a(6) =24a(7) =56a(8) =24a(9) =16a(10) =120a(11) =250a(12) =275a(13) =50a(14) =25a(15) =720a(16) =1884a(17) =1350a(18) =960a(19) =90a(20) =36a(21) =5040a(22) =12348a(23) =14896a(24) =5145a(25) =2695a(26) =147a(27) =49a(28) =40320a(29) =114624