In permutations, we showed that the number of permutations of distinct objects is given by the factorial function How quickly does the factorial function grow as a function of This behavior is captured in the approximation known as Stirling's formula also known as Stirling's approximation.
The factorial function is approximated by
Furthermore, for any positive integer , we have the bounds
Catalan number occurs many times in various counting problems; it is defined to be . For more information, go to Catalan Numbers.