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

Terms

a(0) =1a(1) =2a(2) =10a(3) =6a(4) =36a(5) =186a(6) =24a(7) =168a(8) =1032a(9) =6936a(10) =120a(11) =960a(12) =6840a(13) =53040a(14) =462120a(15) =720a(16) =6480a(17) =52560a(18) =461520a(19) =4499280a(20) =48453840a(21) =5040a(22) =50400a(23) =458640a(24) =4495680a(25) =48449520a(26) =571404960a(27) =7321381200a(28) =40320a(29) =443520