How many rooted plane trees tn are there with n internal nodes? How many rooted plane trees tn are there with n internal nodes? Plane means that left and
right are distinguishable (i.e. mirror images are distinguishable), and rooted simply means
that the tree starts with a single root. For the sake of understanding, the below figure
shows why t3 = 5.


In graph theory and more specifically in rooted plane trees there is a fundamental sentence: The number of rooted plane trees with n nodes equals to n-th Catalan number, that is |Tn| = Cn.
I hope to have helped you.
