Finding the closed form of an infinite series

Question

Consider the infinite series $$S=\sum^\infty_{j=0} \frac{\cos{\left((2j+1)\frac{\pi}{4}\right)}}{(2j+1)^2 \exp((2j+1)^2)}$$ Is there any way I could find the closed form expression? I have considered the limit of this $$S=\lim_{n\to\infty}\sum^n_{j=0} \frac{\cos{\left((2j+1)\frac{\pi}{4}\right)}}{(2j+1)^2\exp((2j+1)^2)}$$ but I don't know how to evaluate this summation.