15. $m(m \geqslant 2)$ people pass a ball to each other, and after receiving the ball, they pass it to someone else. Initially, person A starts with the ball, and this is considered the first pass. Find the number of ways $a_{n}$ for the ball to return to A after $n$ passes.
15. $a_{n}=\frac{(m-1)^{n}}{m}+(-1)^{n} \cdot \frac{m-1}{m}$.