Range for random sequence

There are $n$ ($n>1$) independent and identically distributed random variables whose cumulative distribution function is $$F(x)=\{\begin{array}{ll}0& :x<0\\ x^2& :0\le x\le 1\\ 1& :x>1\end{array}$$ Let $R$ be the range for this random variables (difference between maximum and minimum). Let $E(n)$ be the expected value of $R$. Obviously $E(n)$ is between 0 and 1, furthermore it is rational number. You are given $E(2)=4/15$ and $E(3)=2/5$.

Find $E(20)$. Give your answer rounded to 10 digits after the decimal point.

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Thanks to baihacker for the idea.