Is there any function in python or sage to obtain explicit formula of coefficients for generating functions. For example, Catalan generating function is given as
$${\displaystyle c(x)={\frac {1-{\sqrt {1-4x}}}{2x}}}$$
And I need to obtain general formula for nth coefficient:
$${\displaystyle C_{n}={\frac {1}{2n+1}}{2n+1 \choose n}\,,}$$
