Stirling's Formula
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.
Stirling's Formula
The factorial function is approximated by
Furthermore, for any positive integer , we have the bounds
Central Binomial Coefficient
Catalan Number
Catalan number occurs many times in various counting problems; it is defined to be . For more information, go to Catalan Numbers.