Definition:Pascal's Triangle

Definition
Pascal's Triangle is an array formed by the binomial coefficients:

$\begin{array}{r|rrrrrrrrrr} n & \binom n 0 & \binom n 1 & \binom n 2 & \binom n 3 & \binom n 4 & \binom n 5 & \binom n 6 & \binom n 7 & \binom n 8 & \binom n 9 \\ \hline 0 & 1 & 0 & 0 &  0 &   0 &   0 &  0 &  0 & 0 & 0 \\ 1 & 1 & 1 &  0 &  0 &   0 &   0 &  0 &  0 & 0 & 0 \\ 2 & 1 & 2 &  1 &  0 &   0 &   0 &  0 &  0 & 0 & 0 \\ 3 & 1 & 3 &  3 &  1 &   0 &   0 &  0 &  0 & 0 & 0 \\ 4 & 1 & 4 &  6 &  4 &   1 &   0 &  0 &  0 & 0 & 0 \\ 5 & 1 & 5 & 10 & 10 &   5 &   1 &  0 &  0 & 0 & 0 \\ 6 & 1 & 6 & 15 & 20 &  15 &   6 &  1 &  0 & 0 & 0 \\ 7 & 1 & 7 & 21 & 35 &  35 &  21 &  7 &  1 & 0 & 0 \\ 8 & 1 & 8 & 28 & 56 &  70 &  56 & 28 &  8 & 1 & 0 \\ 9 & 1 & 9 & 36 & 84 & 126 & 126 & 84 & 36 & 9 & 1 \\ \end{array}$

Also see

 * Pascal's Rule
 * Stirling's Triangles