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categories: Combinatorics
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A generating function is a [formal power series](Formal power series) where the coefficient at $x^n$ usually counts the number of combinatorial objects of size $n$.

Sometimes the coefficients are normalized, as is the case with [exponential generating functions](Exponential generating function), where the $n$<sup>th</sup> coefficient is divided by $n!$. This can give the operations on the series a different meaning.

## Problems
- [Bus Routes](https://archive.algo.is/camps/mipt/2015/day6/A/statement.pdf)
- [The Child and Binary Tree](http://codeforces.com/contest/438/problem/E)
- [Devu and Locks](https://www.codechef.com/problems/DEVLOCK)
- [Devu and Birthday Celebration](http://codeforces.com/contest/439/problem/E)
- [Tricolored Coin Fountains](https://projecteuler.net/problem=519)

## See also
- [Formal power series]()