Derivative of Generating Function/General Result/Corollary

Theorem
Let $G \left({z}\right)$ be the generating function for the sequence $\left\langle{a_n}\right\rangle$.

Let $m$ be a positive integer. Let the coefficient of $z^n$ extracted from $G \left({z}\right)$ be denoted:
 * $\left[{z^n}\right] G \left({z}\right) := a_n$

Then:


 * $\left[ z^m \right] \map G z = \dfrac 1 {m!} \map {G^{\paren m} } 0$