I would like to ask the following question:
Let $n$ be a positive integer.
What can you say about
$$\sum (-1)^k {n! \over n_1! n_2! \cdots n_k!}$$
where the sum runs through all $k$ and all sequences $(n_1,n_2,
\ldots, n_k)$ of *POSITIVE* integers such that $n_1 + n_2 + \ldots +
n_k = n$?
Is there a formula for that? Or at least a good upper bound on its
absolute value?
Many thanks in advance,
Dan Haran
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MathIsFun