From my previous question, I changed the sum into:
$\displaystyle \tag*{} \sum \limits ^{\infty}_{n=3,5,7,9....}\dfrac{2n \exp \left(-\pi n/2\right)}{\exp(\pi n)+1}$
Since my previous question, I still couldn't solve this. However, I think there is a solution using elliptical functions or Poisson's Summation formula. But I don't know them. I would still accept answers using them. Any help would be appreciated.