Possible Duplicate:
Asymptotics of $1^n + 2^{n-1} + 3^{n-2} +\cdots + (n-1)^2 + n^1$
About how big is is the sum $\sum_{k=0}^n k^{n-k}$? At the least, can we get an upper bound on it that isn't terrible? (I would consider $(n+1)n^n$, or anything not significantly smaller than it, to be terrible.)