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\vskip 1cm{\LARGE\bf 
A Generalized Ap\'{e}ry Series}
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{\large
M. L. Glasser \\
Department of Physics\\
Clarkson University \\
Postdam, NY 13699-5820\\
USA\\
\href{mailto:laryg@clarkson.edu}{\tt laryg@clarkson.edu}\\
}
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\begin{abstract}
The inverse central binomial series
\begin{equation}S_k(z)=\sum_{n=1}^{\infty}\frac{n^k z^n}{\binom{2n}{n}},
\nonumber
\end{equation}
popularized by Ap\'ery and Lehmer is evaluated for positive 
integers $k$ along with the asymptotic behavior for large $k$. It is found 
that value $z=2$, as commented on by D. H. Lehmer, provides a unique 
relation to $\pi$.
\end{abstract}

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