Solving a recursive equation

Question

So I'm working on a combinatorics problem, to which I've reached that $$f(1)=1, f(n)=1+\frac{1}{n}\sum_{k=1}^{n-1} f(k)$$ I have been working at this problem for a few days now, and I am fairly confident solving this recursive equation is the key to the problem. I tried somehow centering the recursive equation somehow, so that I would be able to solve it, since this is basically the only technique that I have learnt, but this seems completely unusuable for this equation. I notice that the equation diverges, so I am not asking for an asymptotic behavior, but more-so a closed form expression for $f(n)$. I know I haven't shown much of my progress, but thats because I really barely have any when it comes to solving this equation (when it comes to the original problem I guess I have the progress of reaching this equation, which I am confident is correct) Any help would be greatly greatly appreciated.