Abstract: An E-tree is a rooted line-colored tree such that every automorphism of a subtree contain-s ing the root can be extended to an automorphism of the entire tree. When only one color i used, E-trees correspond both to achiral planted trees and to partitions with successively divisible parts. The exact numbers of E-trees with n points and colors from a store of c are found, with and without the restriction that each color should be used at least one. Asymptotic formulas for these quantities are discussed for c fixed and n→∞.