Remarks on the approximation for the number of rooted unordered binary trees

Abstract. The paper investigates the approximation formulas for the unlabeled rooted trees. In the case of ordered binary trees, the number of tree instances can be given with the Catalan numbers. It is an interesting fact, that for the case of unordered trees, only very few works can be found in the literature. The approximation formulas are usually built up with the application of appropriate generator functions. The paper presents an evaluation of a selected approximation formula from the literature.