In this note we compute the generating function for the numbers $\left(\begin{array}{c} {2n} \\ {n} \end{array}\right)^{-1} H_{n} $ in terms of elementary functions ad dilogarithms
@article{479, title = {Power series with inverse binomial coefficients and harmonic numbers}, journal = {Tatra Mountains Mathematical Publications}, volume = {70}, year = {2018}, language = {EN}, url = {http://dml.mathdoc.fr/item/479} }
Boyadzhiev, Khristo N. Power series with inverse binomial coefficients and harmonic numbers. Tatra Mountains Mathematical Publications, Tome 70 (2018) . http://gdmltest.u-ga.fr/item/479/