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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =1a(6) =6a(7) =10a(8) =6a(9) =1a(10) =24a(11) =42a(12) =30a(13) =10a(14) =1a(15) =120a(16) =216a(17) =168a(18) =70a(19) =15a(20) =1a(21) =720a(22) =1320a(23) =1080a(24) =504a(25) =140a(26) =21a(27) =1a(28) =5040a(29) =9360