Number of rooted trees with n points and exactly k specified colors: C(n,k), 1<=n, 1<=k<=n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =10a(5) =9a(6) =4a(7) =44a(8) =102a(9) =64a(10) =9a(11) =196a(12) =870a(13) =1304a(14) =625a(15) =20a(16) =876a(17) =6744a(18) =18200a(19) =20080a(20) =7776a(21) =48a(22) =4020a(23) =50421a(24) =218260a(25) =416500a(26) =362322a(27) =117649a(28) =115a(29) =18766