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

Terms

a(0) =1a(1) =2a(2) =5a(3) =6a(4) =14a(5) =21a(6) =24a(7) =54a(8) =80a(9) =105a(10) =120a(11) =264a(12) =390a(13) =512a(14) =633a(15) =720a(16) =1560a(17) =2304a(18) =3030a(19) =3752a(20) =4473a(21) =5040a(22) =10800a(23) =15960a(24) =21024a(25) =26070a(26) =31112a(27) =36153a(28) =40320a(29) =85680