A closed form for $\sum _{j=0}^{\infty } -\frac{\zeta (-j)}{\Gamma (j)}$ Is there a closed form for 
$$\sum _{j=0}^{\infty } -\frac{\zeta (-j)}{\Gamma (j)}$$
where $\zeta (-j)$ Zeta function and  $\Gamma (j)$ Gamma function.
I tried everything, but I still can not solve it. Any Ideas?

Reflection formula for $\zeta(s)$ transforms the sum into $\sum_{n=1}^{\infty}\left(2\pi i\right)^{-2n}\left(2-4n\right)\zeta\left(2n\right)$. The latter can be computed by differentiating the well-known generating function $\sum_{n=0}^{\infty}\zeta\left(2n\right)z^{2n}=-\frac{\pi z\cot \pi z}{2}$, with the result
$$1-\frac{1}{2\cosh1-2}.$$
