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Integer Combinatoric Functions
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The binomial(n, r) returns the number of subsets of r objects
taken among n objects, i.e. n!/(r! * (n-r)!)

The binomial coefficients are the coefficients of the series expansion
of a power of a binomial, that is ::

    n
   --+    / n \   k             n
   >     |     | x    =  (1 + x)
   --+    \ k /
   k= 0

This leads to the famous pascal triangle. First we expose the OutputForm
domain, which is normally hidden, so we can use it to format the lines. ::

  )set expose add constructor OutputForm

Next we define a function that will output the list of binomial coefficients
right justified with proper spacing: ::

  pascalRow(n) == [right(binomial(n,i),4) for i in 0..n]

and now we format the whole line so that it looks centered: ::

  displayRow(n)==output center blankSeparate pascalRow(n)

and we compute the triangle ::

  for i in 0..7 repeat displayRow i

giving the pretty result: ::
 
   Compiling function pascalRow with type NonNegativeInteger -> List 
      OutputForm 
   Compiling function displayRow with type NonNegativeInteger -> Void 
                                     1
                                  1    1
                                1    2    1
                             1    3    3    1
                           1    4    6    4    1
                        1    5   10   10    5    1
                      1    6   15   20   15    6    1
                   1    7   21   35   35   21    7    1

See Also:

* )show IntegerCombinatoricFunctions
* )d op binomial
* )show OutputForm
* )help set