Using singularity analysis to find the main asymptotic term of the Catalan Numbers
\begin{align} C_n = [z^n]\frac{1-\sqrt{1-4z}}{2z} \end{align}
Can someone please explain to me the general concept of singularity analysis? I understand that you are supposed to find the main singularity (in this case it is when z = 1/4). And then you create a power series expanded about this singularity but I don't know how to do that. Any hints and tips are appreciated.