∆ Определение 1.

Pascal's triangle is a triangular array of numbers such that the $n$-th line consists of $n$ numbers, where each number is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as $0$. The number that is on the $(k+1)$-th place of the $(n+1)$-th line is denoted by $\binom{n}{k}$.