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.


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