documentclass[12 pt]{article}
    usepackage{fullpage}
    usepackage{amsmath}
    usepackage{float}
    usepackage{longtable}
    usepackage{caption}

    begin{document}
     First table is inserted here (longtable).
    begin{longtable}{l l}
    hline
        A & A1             B & B1 \
    hline
    caption*{}label{TableNomen}
    end{longtable}

    newpage
    Second table inserted here.
    begin{table}
    centering
    caption{Influence of X}label{TableC}
    begin{tabular}{c c c c}
hline
    $10^{-5}$ & $80times40$ & 16 & 10         $10^{-4}$ & $80times40$ & 21 & 11 \
hline
    end{tabular}
    end{table}
    newpage
    listoftables
    end{document}

addtocounter{table}{-1}

documentclass{article}
usepackage{longtable}

begin{document}

 begin{longtable}{l l}
   A1 & A2
   addtocounter{table}{-1}
end{longtable}

begin{table}
  centering
  caption{test table}
  label{tab:test}
  begin{tabular}{cc}
  text1 & text2
  end{tabular}
end{table}

end{document}

documentclass[12pt]{article}
usepackage{longtable}
usepackage{caption}
usepackage{hyperref}

begin{document}
 First table is inserted here (longtable).
begin{longtable*}{l l}
hline
    A & A1 \
    B & B1 \
hline
%caption*{Some text}
end{longtable*}

newpage
Second table inserted here.
begin{table}
centering
caption{Influence of X}label{TableC}
...
end{table}

newpage
listoftables
end{document}