Define a rooted tree to be a tree T with a singular node designated as the root of T. (Note that every node in the tree can have an arbitrary number of children.) Each vertex adjacent to the root node of T is itself the root of some tree called a maximal subtree of T. Say two rooted trees T_{1} and T_{2} are similar if there exists some way to cycle the maximal subtrees of T_{1} to get T_{2}. For example, the first pair of trees below are similar but the second pair are not. How many rooted trees with 2019 nodes are there up to similarity?
