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There are n balls in a jar, labeled with numbers 1, 2, ..., n . A total of k balls are drawn, one by one,

There arenballs in a jar, labeled with numbers 1, 2, ...,n. A total ofkballs are drawn, one by one, with replacement, to obtain a sequence ofknumbers.

Find the probability that the sequence obtained is an increasing sequence followed by a decreasing sequence. It is allowed for either of these sequences to be "empty".

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