# Lecture 8: Counting Binary Trees

This lecture provides a proof for the formula for the number of binary trees with n nodes.
It introduces the important concept of generating functions

### Background Material

- Recursion and recurrence relations.
- binomial theorem and binomial coefficients.
- power series.

### Reading

Review the material on generating combinatorial objects in
- Lecture 7 Recursive data structures and algorithm exploration.

Also study Maple's series command.
### Topics

- Recurrence relation for the number of binary trees.
- Binomial theorem.
- Generating function for the number of binary trees.
- Functional equation
- Expanding using the binomial theorem.
- Asymptotics using Stirling's formula

### Lecture Notes

- bintree.pdf - Notes on counting binary trees including review
of the binomial theorem, Stirling's formula, and a derivation of the formula and asymptotics
for the number of binary trees.

### Assignments

Created: Oct. 26, 2006 by jjohnson@cs.drexel.edu