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Pascal's Triangle

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The binomial coefficients

$\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!\,k!} $

can be recursively calculated by

$\displaystyle \binom{n+1}{k} = \binom{n}{k-1} + \binom{n}{k} \,. $

The recursion, known as Pascal's triangle, is illustrated in the figure.

\begin{center} \begin{tabular}{c\vert cccccccccccccc} $\displaystyle \binom{0}{k... ...dots$\ & & $\vdots$\ & & $\vdots$\ & & $\vdots$\ & \\ \end{tabular}\end{center}

(Authors: Höllig/Knesch/Abele)

see also:

[Annotations]
  automatically generated 6/11/2007