Coefficients and Roots of a set of Polynomials

Hi,

who can help further define the coefficients and roots of the
polynomials :

n: Pn=x^(n-1)+A033455*x^(n-2)+??????????????+A000272
------------------------------------------------------------------------------------------------
2: x-1
3: x^2- 8*x+3
4: x^3-34*x^2+56*x-16
5: x^4-104*x^3+505*x^2-500*x+125
6: x^5-259*x^4+3024*x^3-7344*x^2+5616*x-1296
7: x^6-560*x^5+13762*x^4-69580*x^3+117649*x^2-76832*x+16807
...
...
------------------------------------------------------------------------------------------------

The coefficients

a(n-2)= A033455 : (n^5-n)/30= { 0,1,8,34,104,259,560,1092,.....}
a(0) = A000272 : n^(n-2)=
{1,1,3,16,125,1296,16807,262144,......}

are sloan's integer sequence.

Can the other coefficients be determined in a similar form?

Is there a general solution in radicals for these polynomials?
(All roots are on the real axis)

Any comments are welcome.

Gerry

.

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