The problem provided defines a sequence $a_n$ as follows:

$a_n = \frac{n^n}{1 + 2^2 + 3^3 + \dots + n^n}$

The task might involve evaluating the behavior of $a_n$ as $n$ grows larger or simplifying this expression if possible.

Would you like to:

1. Determine the limit of $a_n$ as $n \to \infty$?
2. Calculate specific terms of the sequence (e.g., $a_1, a_2,$ etc.)?
3. Analyze the growth of the denominator in comparison to $n^n$?
4. Explore whether the sequence $a_n$ converges or diverges?
5. Determine an approximation for large $n$?

Let me know if you want a detailed solution or have any questions!

Tip: When dealing with sequences and series, analyzing the terms’ growth rate (e.g., polynomial vs. exponential) often helps in understanding convergence or divergence.