Table read by antidiagonals: T(n,k) = (n*k)!/(n^k*k!), n >=1, k >= 0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =3a(8) =2a(9) =1a(10) =1a(11) =15a(12) =40a(13) =6a(14) =1a(15) =1a(16) =105a(17) =2240a(18) =1260a(19) =24a(20) =1a(21) =1a(22) =945a(23) =246400a(24) =1247400a(25) =72576a(26) =120a(27) =1a(28) =1a(29) =10395