How to use a longtable with only one entry in the list of tables

use for the \endfirsthead the default \caption and for \endhead the starred version of \caption.

In case you want a numbered caption on follow-up table pages, use

\caption{<Caption Text>}
\endfirsthead
\caption[]{<Caption Text>}
\endhead

Minimal working example:

\documentclass{article}

\usepackage{longtable}

\renewcommand*{\arraystretch}{5}% just for the example

\begin{document}

\listoftables

\section{foo}

\begin{longtable}{c}
\caption{A table}
\endfirsthead
\caption[]{A table}
\endhead
bar \\
bar \\
bar \\
bar \\
bar \\
bar \\
bar \\
bar \\
\end{longtable}

\end{document}