I hope this question is not too simple, but I would like to know the asymptotic behaviour of the following function $f: \mathbb{N}^{+} \rightarrow \mathbb{Q}$ where
$$
f(n) = \sum\_{i=1}^{n} \frac{i^n}{n^{4i}}
$$
Any references, pointers, or answers would be most appreciated.



Asymptotics of a function
From the comments so far (including mine above) it follows that
$$ f(n) = \sum\_{i=1}^{n} \frac{i^n}{n^{4i}}=\frac{n!}{(4\ln n)^{n+1}}\left(1+O(n^{-1/2}\ln n)\right). $$


