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.