If I roll a die $100$ times, there are $6^{100}$ possible ordered outcomes.
Some of these outcomes, say $n$, will add to $347$, for example.
Is there a way to express $n$ in terms of Stirling numbers (or am I think of partitions?).
One way to estimate $n$:
note that the sum has a mean of $350$ with a standard deviation of $17.08$.
Use the normal distribution to calculate the probability that the sum is between $346.5$ and $347.5$.
Multiply this probability by $6^{100}$
Does this provide a new (or even useful) way of estimating Stirling numbers?