The ratio of the unsigned coefficients for the discriminants of $x^n+bx+c$ for $n=2$ to $5$ follow a simple pattern:
$\left (\frac{2^2}{1^1},\frac{3^3}{2^2},\frac{4^4}{3^3},\frac{5^5}{4^4} \right )=\left ( \frac{4}{1},\frac{27}{4},\frac{256}{27},\frac{3125}{256} \right )$
corresponding to the discriminants
$(b^2-4c, -4b^3-27c^2,-27b^4+256c^3,256b^5+3125c^4).$
Does the pattern for the ratios extend to higher orders? (An online reference would be appreciated.)