Any ideas on how to approximate and/or simplify this crazy-looking sum will be massively appreciated)
$\frac{1}{\mu}\sum_{j=0}^{\frac{\lambda}{2}} \left(\frac{1}{2}+2\left(\frac{k}{n}\right)^2\right)^j\binom{\frac{\lambda}{2}}{j}\sum_{m=1}^{\mu} \left(\frac{m^2(m+2(\mu-m))^2}{\mu^4}\right)^j\left(1-\frac{m^2(m+2(\mu-m))^2}{\mu^4}\right)^{\frac{\lambda}{2}-j}$