Binomial coefficients

Again for N=20.  The "Table" function in Mathematica makes a list, looping over i from 0 to 20.

In[10]:=

b20 = Table[Binomial[20, i], {i, 0, 20}]

Out[10]=

{1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1}

Type Options[BarChart] to see the various custom settings you can use to change what this next picture looks like.  
We need to load the Graphics`Graphics` package to turn on the BarChart stuff, first.

In[11]:=

<<Graphics`Graphics` ;

In[59]:=

BarChart[b20, BarLabels Range[0, 20] ]

[Graphics:../HTMLFiles/binomial_7.gif]

Out[59]=

⁃Graphics⁃

Created by Mathematica  (September 30, 2003)