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 & \binom n {10} & \binom n {11} & \binom n {12} \\ \hline 0 & 1 &  0 &  0 &   0 &   0 &   0 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 1  & 1 &  1 &  0 &   0 &   0 &   0 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 2  & 1 &  2 &  1 &   0 &   0 &   0 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 3  & 1 &  3 &  3 &   1 &   0 &   0 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 4  & 1 &  4 &  6 &   4 &   1 &   0 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 5  & 1 &  5 & 10 &  10 &   5 &   1 &   0 &   0 &   0 &  0  &  0 &  0 & 0 \\ 6  & 1 &  6 & 15 &  20 &  15 &   6 &   1 &   0 &   0 &  0  &  0 &  0 & 0 \\ 7  & 1 &  7 & 21 &  35 &  35 &  21 &   7 &   1 &   0 &  0  &  0 &  0 & 0 \\ 8  & 1 &  8 & 28 &  56 &  70 &  56 &  28 &   8 &   1 &  0  &  0 &  0 & 0 \\ 9  & 1 &  9 & 36 &  84 & 126 & 126 &  84 &  36 &   9 &  1  &  0 &  0 & 0 \\ 10 & 1 & 10 & 45 & 120 & 210 & 252 & 210 & 120 &  45 &  10 &  1 &  0 & 0 \\ 11 & 1 & 11 & 55 & 165 & 330 & 462 & 462 & 330 & 165 &  55 & 11 &  1 & 0 \\ 12 & 1 & 12 & 66 & 220 & 495 & 792 & 924 & 792 & 495 & 220 & 66 & 12 & 1 \\ \end{array}$

Column
Thus the entry in row $n$ and column $m$ contains the binomial coefficient $\dbinom n m$.

Also see

 * Pascal's Rule
 * Definition:Stirling's Triangles