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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =2a(6) =1a(7) =12a(8) =18a(9) =6a(10) =1a(11) =32a(12) =108a(13) =96a(14) =24a(15) =1a(16) =80a(17) =540a(18) =960a(19) =600a(20) =120a(21) =1a(22) =192a(23) =2430a(24) =7680a(25) =9000a(26) =4320a(27) =720a(28) =1a(29) =448