This problem asks us to find the coefficient of $x^n$ in the power series expansion of a given rational function. This is a classic application of the Binomial Theorem, specifically the expansion of $(1-y)^{-1}$, often combined with partial fraction decomposition.

1. Key Concepts and Formulas

• Binomial Series Expansion: For $|y| < 1$, the expansion of $(1-y)^{-1}$ is given by: $(1-y)^{-1} = 1 + y + y^2 + y^3 + \dots = \sum_{k=0}^\infty y^k$
• Partial Fraction Decomposition: A technique used to decompose a rational function into simpler fractions, which are easier to integrate or expand into series