Derivative of Generating Function/General Result/Corollary

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

Let $m$ be a positive integer. Let the coefficient of $z^n$ extracted from $\map G z$ be denoted:
 * $\sqbrk {z^n} \map G z := a_n$

Then:


 * $\sqbrk {z^m} \map G z = \dfrac 1 {m!} \map {G^{\paren m} } 0$

where $G^{\paren m}$ denotes the $m$th derivative of $G$.