Pascal's Triangle is a triangular array of numbers where each number is the sum of the two directly above it. The edges of the triangle are all 1s.

Construction:

The entry in the n-th row and k-th position is denoted by the binomial coefficient $\binom{n}{k}$.

$$ \binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k} $$

The rows are conventionally enumerated starting with row $n=0$ at the top.

Properties:

• The sum of the numbers in any row is $2^n$.
• The numbers in each row correspond to the coefficients of the binomial expansion of $(x+y)^n$.
• The diagonals contain interesting sequences, like the triangular numbers.