Code in python using recursion

Purpose The programming assignment will provide an exercise in using recursion. There are two problems which need to be solved. The first asks for a recursive function to calculate a Catalan number. The second is to solve a path-finding problem in two dimensional space. The assignment will require the usage of recurrence as well as good class design. Problem 1: The good Mr. Catalan. The Catalan number form a sequence of natural numbers that occur in many counting problems. They are named after the mathematician Eugene Charles Catalan (http://en.wikipedia.org/wiki/Eug%C3%A8ne Charles Catalan) and are defined by the following recursive formula: n Co = 1 and Cn+1 = > CiCn-i for n 2 0; 1=0 Write a program called Catalan which takes one argument and calls a recursive function which computes the nth Catalan number. The program then prints out the result to the console. For instance, python catalan.py 4 Would print out: 14 python catalan.py 10 Would print out: 16796