I'm physicist, in my work on BEC i have encountered infinite sum, which i expect could be expressed as analytic function. I ask for your help, any hints will be very helpful. Best regards.

$\sum_{kl}^{\infty}\sum_{ij}^{\infty}\frac{1}{A\exp(ak+bl+2ci+d)+1}\frac{1}{A\exp(ak+bl+c(2j+1)+d)+1} \frac{1}{4^{i+j}}\frac{(2i)!(2j+1)!}{(i!)^{2}(j!)^{2}(2j+1-2i)^{2}}$

A, a, b, c, d are positive constants.