The topic is an introduction to generating functions and some of their uses in discrete mathematics.

In discrete mathematics, many problems /questions have the answer in the form of a sequence. Generating functions offer a method for ‘getting’ the sequence. Naturally, what is meant by getting a sequence is to obtain an explicit and simple formula for the sequence. However, many sequences are so complex that simple explicit formulas cannot be obtained. For example, the n-th term of the sequence of prime numbers, 2, 3, 5, 7, 11, …., cannot be expressed in explicit form.

Although an explicit formula cannot be obtained, we should still expect to get more information about the behavior of the sequence.

Generatingfunctionology offers a tool for extracting much information about a sequence, not just in the form of an explicit formula.