Triangle, read by rows, T(n,k) = Sum_{j=1..k} binomial(n-1, j-1)*binomial(k, j - 1)*(j-1)!.

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =5a(5) =13a(6) =1a(7) =7a(8) =28a(9) =73a(10) =1a(11) =9a(12) =49a(13) =185a(14) =501a(15) =1a(16) =11a(17) =76a(18) =381a(19) =1426a(20) =4051a(21) =1a(22) =13a(23) =109a(24) =685a(25) =3331a(26) =12607a(27) =37633a(28) =1a(29) =15