# Maximum value of generic polynomial with evenly spaced roots on interval [0, 1]

Is there a compact form for value:

$$V_n = \max_{0 \le x \le 1} \left| \prod_{i=0}^n \left(x-\frac{i}{n}\right)\right|$$

I calculated $$V_1=\frac{1}{4}, V_2=\frac{1}{12\sqrt3}, V_3=\frac{1}{81}$$, but I don't see a pattern. Some resonable upper-bounds (dependent of $$n$$) also will be helpful.