RootSum Sequences

[franktaw at netscape.net]

That should, of course, be "Start with a monic polynomial ...".

The sequence generated in this way will have a rational generating 
function.  If P(x) is the polynomial, and P'(x)  is its derivative, the 
g.f. is P'(1/x) / (x P(1/x));  or equivalently R[P'(x)]/R[P(x)] where R 
is the operator that reverses the order of the coefficients of a 
polynomial.

Franklin T. Adams-Watters


-----Original Message-----
From: Ed Pegg Jr <edp at wolfram.com>

Start with a polynomial with integer coefficients, and find it's roots. 
The sum of these roots, and the 
sums of the powers of these roots, is an integer. 
 
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