For the non-homogeneous recurrence $a_n = 3a_{n-1} - 2a_{n-2} + (n+1) \cdot 2^n,$ the homogeneous part has characteristic roots $r_1 = 2$ and $r_2 = 1$. Since $r_1 = 2$ is a root and the forcing term is $(n+1) \cdot 2^n$, what form should the particular solution $a_n^{(p)}$ take?