Definition:Generating Function/Extraction of Coefficient

Definition

Let $\map G z$ be the generating function for the sequence $S = \sequence {a_n}$.

The coefficient of $z^n$ extracted from $\map G z$ is the $n$th term of $S$, and can be denoted:

$\sqbrk {z^n} \map G z := a_n$

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.9$: Generating Functions: $(31)$