Macsyma is a symbolic manipulation system with origins in the 1960s.
Download its current freeware implementation from 

	 http://maxima.sourceforge.net/download.html

When you have installed it on your computer, you can do things like
obtain the formulas for recursively-defined function.  For example,
the Chebyshev polynomials may be obtained by the commands

  t[0,x]:1; 
  t[1,x]:x; 
  t[n,x]:= 2*x*t[n-1,x]-t[n-2,x];

The ":" assignment command evaluates the expression on the right
first, while the ":=" assignment command waits so that recursive
expressions may be expanded.

To print the first 21 Chebyshev polynomials, use

  for n:0 thru 20 do print(expand(t[n,x]));