RootSum Sequences

[Ed Pegg Jr]

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.

So, some examples, starting with x^3 - 6 x^2 + 4 x - 2.

Table[RootSum[#^3 - 6 #^2 + 4 # - 2 &,#^n &],{n,1,20}]

6, 28, 150, 800, 4256, 22636, 120392, 640320, 3405624, 18113248, 
96337632, 512384048,
2725180256, 14494220608, 77089370720, 410009702400, 2180689172736, 
11598274968256,
61686912523392, 328089753612800

Table[RootSum[4+12*#1-6*#1^2-8*#1^3+#1^4+#1^5&, #^n&],{n,1,20}]

{-1, 17, -7, 89, -51, 521, -379, 3201, -2851, 20137, -21275, 128369, 
-156339, 825401,
-1131147, 5340993, -8075171, 34736777, -57020027, 226895889}

Table[RootSum[4+4*#1-6*#1^2-#1^3+#1^4&, #^n&],{n,1,20}]

{1,13,7,65,51,361,379,2081,2707,12233,18635,72881,124931,438745,822267,2663489,
5342387,16279273,34390571,100042705}

Are there any polynomials that give some OEIS Sequences?  As an aside, 
those last two polynomials
are factors of the characteristic polynomial of the Balaban 11-cage.  I 
wondered if the two polynomials
were related in some strange way... and I then noticed they shared {1, 
7, 51, 379} in their sequences.

Ed Pegg Jr.