# How do I find the nth row of Pascal's triangle?

Jul 15, 2015

The $n$th row of Pascal's triangle is:

$\left(\begin{matrix}n - 1 \\ 0\end{matrix}\right)$ $\left(\begin{matrix}n - 1 \\ 1\end{matrix}\right)$ $\left(\begin{matrix}n - 1 \\ 2\end{matrix}\right)$... $\left(\begin{matrix}n - 1 \\ n - 1\end{matrix}\right)$

That is:

((n-1)!)/(0!(n-1)!) ((n-1)!)/(1!(n-2)!) ... ((n-1)!)/((n-1)!0!)

#### Explanation:

It's generally nicer to deal with the $\left(n + 1\right)$th row, which is:

$\left(\begin{matrix}n \\ 0\end{matrix}\right)$ $\left(\begin{matrix}n \\ 1\end{matrix}\right)$ $\left(\begin{matrix}n \\ 2\end{matrix}\right)$ ... $\left(\begin{matrix}n \\ n\end{matrix}\right)$

or if you prefer:

(n!)/(0!n!) (n!)/(1!(n-1)!) (n!)/(2!(n-2)!) ... (n!)/(n!0!)