Let $f:\mathbb{N} \rightarrow \mathbb{N}$ such that $f(1)=2011$ and $f(n)= \frac{1}{n^2 -1}(f(1)+f(2)+...+f(n-1))$ for $n \ge 2$. Calculate $f(2011)$
Solving for $f(2004)$ in a given functional equation