Triangle of number of labeled rooted trees with n nodes and k leaves, n >= 1, 1 <= k <= n.

Terms

a(0) =1a(1) =2a(2) =0a(3) =6a(4) =3a(5) =0a(6) =24a(7) =36a(8) =4a(9) =0a(10) =120a(11) =360a(12) =140a(13) =5a(14) =0a(15) =720a(16) =3600a(17) =3000a(18) =450a(19) =6a(20) =0a(21) =5040a(22) =37800a(23) =54600a(24) =18900a(25) =1302a(26) =7a(27) =0a(28) =40320a(29) =423360