T(n,m) = binomial(m!,n).

Terms

a(0) =1a(1) =2a(2) =0a(3) =6a(4) =1a(5) =0a(6) =24a(7) =15a(8) =0a(9) =0a(10) =120a(11) =276a(12) =20a(13) =0a(14) =0a(15) =720a(16) =7140a(17) =2024a(18) =15a(19) =0a(20) =0a(21) =5040a(22) =258840a(23) =280840a(24) =10626a(25) =6a(26) =0a(27) =0a(28) =40320a(29) =12698280