Array t(n,m)=(n*m)!/(n + m - 1)! read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =1a(6) =1a(7) =30a(8) =30a(9) =1a(10) =1a(11) =336a(12) =3024a(13) =336a(14) =1a(15) =1a(16) =5040a(17) =665280a(18) =665280a(19) =5040a(20) =1a(21) =1a(22) =95040a(23) =259459200a(24) =4151347200a(25) =259459200a(26) =95040a(27) =1a(28) =1a(29) =2162160