Quote:
Originally Posted by R.D. Silverman
It was tedious to do by hand. i.e. please verify that f(2z + 1/z) equals
the 12th degree polynomial divided by z^6.

Using PariGp I've gotten:
(22:20) gp > f(x)=x^6+2*x^510*x^420*x^3+16*x^248*x+72
(22:20) gp > substpol(f(x),x,2*z+1/z)
%7 = (64*z^12 + 64*z^11 + 32*z^10  16*z^8  176*z^7 + 56*z^6  8*z^5  4*z^4 + 2*z^2 + 2*z + 1)/z^6
(22:20) gp >
So there are errors in your polynom.