Some comments from Jose

1. You should review Taylor series (from MATH 126) and make sure you can recognize the expansions of important functions such as geometric, trigonometric, exponential, and logarithmic functions.
2. When trying to express a generating function as a rational function there should be *NO* n in your final expression. 'N' is usually a dummy variable and has NO meaning.
3. Generating functions are an excellent tool, but they have a problem: you have to be VERY careful with the indices to avoid making mistakes.
4. When you solve a recurrence using a sophisticated method like generating functions you should check your formula. Compute by hand the first few terms and make sure the formula gives the right answer.