Need some hints for generating function-assignment.

Question

I have this assignment:

Which number sequence have the function :

$$f(x) = \frac{1}{1+2x}$$

as its generating function?

I don't know where to start here. I'm stuck at the very start and need some hints to get me on the right path.

Answer 1

Hint :

1. What is the generating function of :

$$f(X):=\frac{1}{1-X} $$

2. Then what is the generating functio for $f(\lambda X)$ if $\lambda\in\mathbb{R}$.

3.Conclude using the fact that $f(-2X)$ is exactly the function you are looking for.