Number of Partitions as Coefficient of Power Series

Theorem
The number of partitions $p \left({n}\right)$ of a (strictly) positive integer $n$ is equal to the coefficient of $x^n$ when the expression:
 * $f \left({n}\right) = \dfrac 1 {\left({1 - x}\right) \left({1 - x^2}\right) \left({1 - x^3}\right) \cdots}$

is expanded into a power series.

That is:
 * $f \left({n}\right) = 1 + p \left({1}\right) x + p \left({2}\right) x^2 + p \left({3}\right) x^3 + \cdots$