Arithmetic overflow in TiKZ/pgfmath

Question

I am writing some material on the trinomial theorem and Pascal's pyramid, and I'm trying to typeset a single layer. Here is my code so far:

\documentclass{article}

\usepackage{tikz}

\begin{document}
\pgfkeys{/pgf/number format/.cd,int trunc}

\small
\begin{tikzpicture}
  \pgfmathsetmacro{\n}{8}
  \foreach \i in {0,1,...,\n}
  {
    \foreach \j in {0,...,\i}
    {
      \draw (\j-\i*0.5,\i*0.866,) -- ++(1,0) -- ++(-0.5,-0.866) -- cycle;
      \node[align=center] at (0.1+\j-\i*0.5,-0.65+\i*0.866)
      {\pgfmathparse{factorial(\n)/factorial(\n-\i)%
       /factorial(\j)/factorial(\i-\j)}\pgfmathprintnumber{\pgfmathresult}};
    }
  }
\end{tikzpicture}

\end{document}

This works fine up to n=7, but crashes with an arithmetic overflow on n=8. As you can see, the computation is simply finding the values of some multinomial coefficients. But why the crash on n=8? And what's the best way around it?