Triangle read by rows: t(n,m)=If[m*(n - m) == 0, 1, n!*(1 - 1/Binomial[n, m])].

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =4a(8) =4a(9) =1a(10) =1a(11) =18a(12) =20a(13) =18a(14) =1a(15) =1a(16) =96a(17) =108a(18) =108a(19) =96a(20) =1a(21) =1a(22) =600a(23) =672a(24) =684a(25) =672a(26) =600a(27) =1a(28) =1a(29) =4320