documentclass[border=10]{standalone}

usepackage{tikz}
usepackage{pgfplots}
pgfplotsset{compat=1.9}

begin{document}
  % Explicit formula
  pgfmathdeclarefunction{explicit_sum}{1}{%
    pgfmathparse{(#1*(#1-1))/2}%
  }

  % The inner function
  pgfmathdeclarefunction{square}{1}{%
    pgfmathparse{#1*#1}%
  }

  % Compute the sum of another function
  % Does not work...
  pgfmathdeclarefunction{manual_sum}{1}{%
    %Parameter should be integral
    pgfmathtruncatemacrocnt{10*#1}
    pgfmathsetmacroret{0}
    foreach i in {1,...,cnt} {
      pgfmathsetmacroret{ret + sum(i)}
    }
    pgfmathparse{ret}
  }

  begin{tikzpicture}
    begin{axis}
      % Expected
      addplot[samples at={1,...,10}] {explicit_sum(x)};

      % Does not work
      addplot[samples at={1,...,10}] {manual_sum(x)};
    end{axis}
  end{tikzpicture}

end{document}