# Number of Distinct Values of $$f(n)$$

Algebra Level 4

$\large f(n) = \sum_{k =0}^{n}\frac{(-1)^{n+k}(k+1)^n}{k!(n-k)!}$

Let $$n$$ be a positive integer, find the number of distinct values of $$f(n)$$.

Notation: $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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