Array read by antidiagonals: T(m,n) = Sum_{i=1..m} i*(n-1+i)!.

Terms

a(0) =1a(1) =2a(2) =5a(3) =6a(4) =14a(5) =23a(6) =24a(7) =54a(8) =86a(9) =119a(10) =120a(11) =264a(12) =414a(13) =566a(14) =719a(15) =720a(16) =1560a(17) =2424a(18) =3294a(19) =4166a(20) =5039a(21) =5040a(22) =10800a(23) =16680a(24) =22584a(25) =28494a(26) =34406a(27) =40319a(28) =40320a(29) =85680