Re: Do these polynomials look familiar to anyone?

In article <1191178939.992157.304700@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Daniel Fetchinson <fetchinson@xxxxxxxxxxxxxx> wrote:

I recently came across the following polynomials and was wondering if
they were in any way related to "famous" polynomials with known
coefficients for arbitrary order:

p[1] = - x - 6/5;

p[2] = x^2 + 37/15 x - 8/5

p[3] = - x^3 - 79/21 x^2 + 517/105 x - 16/7

p[4] = x^4 + 71/14 x^3 - 52537/5250 x^2 + 2307/250 x - 24/7

p[5] = - x^5 - 115/18 x^4 + 265577/15750 x^3 - 1096469/47250 x^2 +
14787/875 x - 16/3

p[6] := x^6 + 347/45 x^5 - 1405328/55125 x^4 + 38529868/826875 x^3 -
41502437/826875 x^2 + 2819816/91875 x - 128/15

Can anyone see any pattern? (Apart from the leading and constant terms
for which a general formula is quite obvious.)

Cheers,
Daniel


A doesn't seem to satisfy a three-term recurrence, as orthogonal
polynomials do.
.

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