A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted
trees of
nodes is ,
where
is the number of rooted trees of vertices (Harary 1994, pp. 188-190), so there are 0,
1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, ... (OEIS A000081)
planted trees of ,
2, 3, ... vertices.
nodes is 
,
where 
is the number of rooted trees of 
vertices (Harary 1994, pp. 188-190), so there are 0,
1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, ... (OEIS A000081)
planted trees of 
,
2, 3, ... vertices.
