Hello community! The problem you see above is a combinatorial problem that I could not solve. :c
This problem seemed easy to me at first like there are people $1,2,3, \ldots, n$ sitting on a circular table and I thought that it was easy using casework and stuff. However, when I really started doing this problem, this problem seemed harder than I thought. I thought about complementary counting but that clearly won't help. From the example given above, I tried first adding singleton sets: $n$. But how do I find out the number of sets with two elements and so on? Recursion?? I really don't know.
Any help would be much appreciated. Thanks.