Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) i * ( n + 2(i-1) )!

Terms

a(0) =1a(1) =2a(2) =13a(3) =6a(4) =50a(5) =373a(6) =24a(7) =246a(8) =2210a(9) =20533a(10) =120a(11) =1464a(12) =15366a(13) =163490a(14) =1834933a(15) =720a(16) =10200a(17) =122424a(18) =1466886a(19) =18307490a(20) =241335733a(21) =5040a(22) =81360a(23) =1098840a(24) =14637624a(25) =201050886a(26) =2892317090a(27) =43830481333a(28) =40320a(29) =730800