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The bound formula is:

$H(M,N,n,k) \leq (( \frac{p}{p+t} )^{p+t} (\frac{1-p}{1-p-t})^{1-p-t})^n$

So how to proof it?

Some papers discuss it: this one, that one.

They say the proof is in the following paper: The tail of the hypergeometric distribution. Discrete Mathematics

But I can not find the online version.

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    @Didier Thank you for your explaination.2011-02-14

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This question has been answered to the satisfaction of the OP in the comments.