A

Step 1: Let's analyze the problem.
The total distance travelled by a ball that rebounds after hitting the ground involves the distance dropped and the distances of subsequent bounces.
For each bounce, the ball rises to a height reduced by the coefficient of restitution (e) and travels twice that height (up and down). Thus, for n bounces, the total distance will be:
- Down to 0: h0
- For each bounce, the up distance is e^i * h0 (i = 1 to n). The total distance from bounces becomes:
Distance = h0 + 2 * (e * h0 + e^2 * h0 + ... + e^n * h0)
This is a geometric series:
Sum = h0 [1 + 2 * (e + e^2 + e^3 + ... + e^n)] = h0 [1 + 2 * e * { (1 - e^n) / (1 - e) }]
Step 2: After including all fractions, simplifying gives total distance travelled as e^2n * h0.
Therefore, the correct answer is [A] e^2n h0.