]> $$\zeta \left(s\right)=\frac{-1}{s^n\left(1-2^{1-s}\right)}\sum _{j=0}^{2n-1}\frac{e_j}{{\left(j+1\right)}^s}+\gamma \left(s\right);e_j={\left(-1\right)}^j\left(\sum _{k=0}^{j-n}\frac{n!}{k!\left(n-k\right)!}-2^n\right)\wedge \left|{\gamma }_n\left(s\right)\right|<=\frac{1}{8^n|1-2^{1-s}|}$$