\begin{definition}[Definition:Pascal's Triangle/Diagonal]
Consider Pascal's Triangle:
{{:Definition:Pascal's Triangle}}
The $n$th '''diagonal''' of Pascal's triangle consists of the entries $\dbinom {n + m} m$ for $m \ge 0$:
:$\dbinom n 0, \dbinom {n + 1} 1, \dbinom {n + 2} 2, \dbinom {n + 3} 3, \ldots$
Hence the '''diagonal''' leading down and to the right from $\dbinom 0 0$, containing all $1$s, is identified as the '''zeroth diagonal''', or '''diagonal $0$'''.
\end{definition}