Final answer:
The question involves solving a recurrence relation, which typically requires finding both the homogeneous and particular solutions. The reference to series expansions and binomial theorem does not directly aid in solving this particular recurrence relation. To provide a solution, one would need to find the homogeneous solution to the recurrence and then guess a particular solution to address the non-homogeneous part.
Step-by-step explanation:
The question asks to solve the recurrence relation an = 4an-1 - 64 + 3n + 2n. Solving this recurrence requires knowledge of series expansions and potential methods for dealing with homogenous and particular parts of the recurrence separately. Unfortunately, the information provided above regarding series expansions such as the binomial theorem does not directly relate to solving the given recurrence. The question might be referring to finding a closed form of the sequence defined by this recurrence relation, which is typically done by finding the homogeneous solution, then finding a particular solution, and combining the two to get the general solution.
To solve this, we would begin by finding a homogenous solution to the part an = 4an-1, which is a geometric sequence that can be addressed using series expansions. Next, we address the non-homogeneous part -64 + 3n + 2n by guessing a particular solution that fits the form of these terms. We could look for a solution in the form of An2 + Bn + C + D2n and then determine the constants A, B, C, and D that satisfy the original equation.