解决方案：
\renewcommand\thetable{\Roman{table}}
演示效果：


演示代码：
\documentclass{book}
\usepackage[font=small,format=plain,labelfont={bf,up},labelsep=space]{caption}

% Change "Table" to "TABLE" in tables, but leave \autoref intact
\DeclareCaptionLabelFormat{table}{TABLE~#2}
\captionsetup[table]{labelformat=table}

% Change the numbering scheme from "1.3" to "III"
   \captionsetup{tablewithin=none}
   \renewcommand\thetable{\Roman{table}}

    \begin{document}

    \begin{table}[!ht] \def\B#1{$\displaystyle{n\choose#1}$}
    \begin{center} \begin{tabular}{c|cccccccc}
    $n$&\B0&\B1&\B2&\B3&\B4&\B5&\B6&\B7\\hline
    0 & 1\\
    1 & 1&1\\
    2 & 1&2&1\\
    3 & 1&3&3&1\\
    4 & 1&4&6&4&1\\
    5 & 1&5&10&10&5&1\\
    6 & 1&6&15&20&15&6&1\\
    7 & 1&7&21&35&35&21&7&1
    \end{tabular} \end{center}
    \caption{Pascal's triangle. }
    \end{table}

    \end{document}