Final answer:
To solve the recurrence relation using generating functions, define a generating function A(x) as the power series representation of the sequence aₖ. Then, multiply the recurrence relation by xₖ and sum over all values of k, resulting in a generating function equation. Solve this equation using the initial conditions to find A(x) and determine the values of aₖ from its coefficients.
Step-by-step explanation:
To solve the recurrence relation using generating functions, we can define the generating function A(x) as the power series representation of the sequence aₖ.
Multiplying the entire recurrence relation by xₖ and summing over all values of k, we obtain a generating function equation. Using the initial conditions, we can solve this equation for A(x).
From the coefficients of A(x), we can then determine the values of aₖ.