I just started learning how to use generating functions to solve a recurrence relation. But I have some questions.
Suppose that I have a recurrence relation that has the rational function:
$$f(x) = \dfrac{P(x)}{Q(x)} $$
As far I know, I have to find the $n$th term of the generating function.
My question is:
Is it true to simply calculate the $n$th coefficient of the Taylor series of $f(x)$ ?
For example I asked a question here. How can I use that to solve the recurrence relation?
edit: Just to clarify: Using some CAS package, like, Sympy is it sufficient to find the $n$th coefficient of the Taylor series without decomposing the function $f(x)$ to partial fractions?