Catalan Number
From charlesreid1
Very important number series occurring in combinatorics: https://en.wikipedia.org/wiki/Catalan_number
Recurrence relation:
$ C_0 = 1 $
$ C_{n+1} = \sum_{i=0}^{n} C_{i} C_{n-i} $
Formula:
$ C_{n} = \dfrac{(2n)!}{(n+1)! n!} $
More links:
- Wikipedia link (also above): https://en.wikipedia.org/wiki/Catalan_number
- geeks for geeks, focusing on programming implementations (non-recursive and recursive): http://www.geeksforgeeks.org/program-nth-catalan-number/
- interview repo on github: https://github.com/mission-peace/interview/blob/master/src/com/interview/dynamic/CountNumberOfTreesInBST.java