Given a generating function $F(z)$, am I right to say that the coefficient $a_k$ of $[z^n]$ is computed by $\frac{F^{(k)}(0)}{k!}$ $(1)$.
Since we have the definition of $F(z)$ is:
$F(z) = \sum_{i > 0}{a_i*z^i}$
Differentiate $F(z)$ $i$ times then I have $(1)$.
However, do we have any approximation of $a_k$ when $k$ is large, since I don't think compute differentiation of $F(z)$ 100 times is an easy work.
Thanks,