Catalan Number

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