In a recent work, Dancs and He found new formulas for $\ln 2$ and $\zeta(2n+1)$, $n$ being a positive integer, which are expressed in terms of Euler polynomials, each containing a series that apparently cannot be evaluated in closed form, distinctly from $\zeta(2n)$, for which Euler's formula allows us to write it as a rational multiple of $\pi^{2n}$. There in that work, however, the formulas are derived through certain series manipulations, by following Tsumura's strategy, which makes it curious — in the words of those authors themselves — the appearance of the number $\ln 2$. In this note, I show how some known zeta-series can be used to derive the Dancs-He series in an alternative manner.