Solving a differential equation using power series

Let and let

be a solution to the differential equation:

The first question asks: "What is the set of possible values for ?" For which i have found that

and

The second question (the one I'm stuck on) asks: "By substituting (1) into (2) for each value of found in the previous question determine the corresponding coefficient in (1). I have somewhat done this and got this equation:

Where do I go from here? Is my equation even right in the first place?