I have the following sum:
$$ \sum_{k=1}^{V} (-1)^{k-1} \frac{{V \choose k}^A}{{DV \choose k}^{A-1}} $$
Is there an approximation available for this sum? I computed this sum with python for different values of D, V, A and it seems to be very close to $\frac{V}{D^{A-1}}$. I used numbers like D = 30, V = 4, A = 3. I tried to read this:
but I did not understand the notation well.
Is there a way to compute this? Is $\frac{V}{D^{A-1}}$ a good approximation of it? Thank you!