Pascal's triangle

Description

Pascal's triangle is the triangular array of the binomial coefficients. Its rows are numbered $n = 0, 1, 2, \dots$ from the top. Row $n$ has $n + 1$ entries, $\binom{n}{0}, \binom{n}{1}, \dots, \binom{n}{n}$, from left to right.

The first five rows are these. $$\begin{array}{ccccccccc} & & & & 1 & & & & \\ & & & 1 & & 1 & & & \\ & & 1 & & 2 & & 1 & & \\ & 1 & & 3 & & 3 & & 1 & \\ 1 & & 4 & & 6 & & 4 & & 1 \end{array}$$

Each row starts and ends with $1$. Each other entry is the sum of the two entries next to it in the row above, by Pascal's rule.