On Series of Transformed Zeta Function

We transform a zeta function to the alternative sum asζ∗(s) =∑∞n=1(−1)nnsand represent it assome series, for example∞∑n=1(s)2nζ∗(s+ 2n)(2n)!22n,∞∑n=1(s+ 1)2nζ∗(s+ 2n)(2n)!22n,etc., where (s)n=s(s+ 1)···(s+n−1), Re(s)>1, and we obtain their formulas.