Triangle T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2, read by rows.

Terms

a(0) =2a(1) =1a(2) =2a(3) =2a(4) =4a(5) =2a(6) =6a(7) =12a(8) =9a(9) =2a(10) =24a(11) =48a(12) =40a(13) =16a(14) =2a(15) =120a(16) =240a(17) =210a(18) =100a(19) =25a(20) =2a(21) =720a(22) =1440a(23) =1296a(24) =672a(25) =210a(26) =36a(27) =2a(28) =5040a(29) =10080