Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =8a(5) =9a(6) =24a(7) =30a(8) =32a(9) =33a(10) =120a(11) =144a(12) =150a(13) =152a(14) =153a(15) =720a(16) =840a(17) =864a(18) =870a(19) =872a(20) =873a(21) =5040a(22) =5760a(23) =5880a(24) =5904a(25) =5910a(26) =5912a(27) =5913a(28) =40320a(29) =45360