Certain double series of Euler type and of Eisenstein type and Hurwitz numbers

Special values of the Lerch zeta function for $j\geq 2 $ are given by $\sum $ $\frac{e^{2\pi inz}}{(n\tau)^{j}}=-\frac{\mathcal{B}_{j}(z;\tau)}{j!}$, (1.1) $n\in Z\backslash \{0\}$ where $B_{j}(z) $ is the ordinary jth Bemoulli polynomial an