Array read by antidiagonals: T(n,k) = (k+1)^n*(n+k)!.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =2a(6) =6a(7) =24a(8) =18a(9) =6a(10) =24a(11) =192a(12) =216a(13) =96a(14) =24a(15) =120a(16) =1920a(17) =3240a(18) =1920a(19) =600a(20) =120a(21) =720a(22) =23040a(23) =58320a(24) =46080a(25) =18000a(26) =4320a(27) =720a(28) =5040a(29) =322560