A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent to oriented trees. A tree which is not rooted is sometimes called a free tree, although the unqualified term "tree" generally refers to a free tree. A rooted tree in which the root vertex has vertex degree 1 is known as a planted tree. The numbers of rooted trees on n nodes for n = 1, 2, ... are 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, ... (OEIS A000081). Denote the number of rooted trees with n nodes by T_n, then the generating function is T(x) | congruent | sum_(n = 0)^∞ T_n x^n | = | x + x^2 + 2x^3 + 4x^4 + 9x^5 + 20x^6 + 48x^7 + 115x^8 + 286x^9 + 719x^10 + ....

free tree | ordered tree | planted tree | red-black tree | rooted graph | tree | weakly binary tree