Definition:Generating Function/Extraction of Coefficient

Let $G \left({z}\right)$ be the generating function for the sequence $S = \left\langle{a_n}\right\rangle$.
The coefficient of $z^n$ extracted from $G \left({z}\right)$ is the $n$th term of $S$, and can be denoted:
$\left[{z^n}\right] G \left({z}\right) := a_n$