Find the sequences given their generating function $$1)\ \ f(x)=\frac{1}{1+x^2} \\ 2)\ \ \ f(x)=\frac{1}{(x-2)^2}$$
How computing these two examples will be different from each other? They vary from the standard examples when the quadratic equation has 2 solutions. How to start with only basic equation $f(x)=\frac{1}{1-x}=1+x+x^2...$ ?
The hint for (1) is the substitution $u=-x^2$.
The hint for (2) is to find the series for the function without the square and then differentiate function and series.