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

Terms

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