MathNet 2017-part-01 — 176 problems (EN–VI) Question 48

We have $n$ students sitting at a round table. Initially each student is given one candy. At each step each student having candies either picks one of its candies and gives it to one of its neighbouring students, or distributes all of its candies to its neighbouring students in any way he wishes. A distribution of candies is called legal if it can be reached from the initial distribution via a sequence of steps.
Determine the number of legal distributions. (All the candies are identical.)