Does it have some closed form or approximation ? I tried on my own but i am not getting any idea regarding this.
$$\sum_{k_1=k}^{M}\sum_{k_2=k}^{M}\frac{k_1^{-\gamma} k_2^{-\gamma} {{M-k}\choose{k_1-k}}{{M-k_1}\choose{k_2-k}}}{{M\choose k_1}{M \choose k_2}}$$ One implied relation is "$k_1+k_2 \leq M+k$".
Please share hint or solution or direction.