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\documentclass{standalone}
\standaloneconfig{margin=0.5cm}

\usepackage{tikz}
\usepackage{xintexpr}

\begin{document}

\begin{tikzpicture}
   \foreach \n in {0,...,5} {
      \node at (0,-\n) {\n:};
      \foreach \k in {0,...,\n} {
         \node at (\k+0.5,-\n) {$\xintexpr\xintiiBinomial{\n}{\k}\relax$};
      }
   }
\end{tikzpicture}

\end{document}


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