def: $\gamma(k)=\frac{\sqrt2^k}{\sqrt\pi}\Gamma(\frac{k+1}{2})$
$m_l$ are integers and $|m_l|<M$, $k_l$ are positive integer and $\sum_{l}k_l=k,\sum_{l}k_lm_l=s$.In other words, decompose $s$ into the sum of some integers $m_l$ with given bounds $M$, where $k_l$ is its multiplicative number and the total number of integers is $k$
Estimate the oder of $k$ for maximum of: $$\prod_{l}\frac{\gamma(k_l)}{(2\pi|m_l|)^{k_l}}$$
I come to this question when I want to prove a coefficient is well defined by the given expression sum over k.
