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In Mathematica:

Sum[((365!/(365 - k)!)) * k * StirlingS2[N, k], {k, 1, N}] / 365^N

StirlingS2 is a Stirling Number of the Second Kind:

http://en.wikipedia.org/wiki/Stirling_number_of_the_second_kind

Or you could just do 365*(1- (364/365)^N) LOLZ.

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14y ago
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