Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, with formal power series that often correspond to analytic functions.
Given a generating function, analytic combinatorics attempts to describe the asymptotic behavior of a counting sequence using algebraic techniques. This often involves analysis of the singularities of the associated analytic function.
Two types of generating functions are commonly used — ordinary and exponential generating functions.
An important technique for deriving generating functions is symbolic combinatorics.