In the following problem we, as usual, define $\displaystyle 0^0 = 1.$

Evaluate $\displaystyle \sum_{j=1}^n \binom{n}{j}(j-1)^{j-1}(n-j)^{n-j}$.

In case you want to see if your final answer is correct or not:

Spoiler:

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- Apr 7th 2009, 10:22 PMNonCommAlgAn identity
In the following problem we, as usual, define $\displaystyle 0^0 = 1.$

Evaluate $\displaystyle \sum_{j=1}^n \binom{n}{j}(j-1)^{j-1}(n-j)^{n-j}$.

In case you want to see if your final answer is correct or not:

__Spoiler__: