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

rooted tree | tree