Nice way to express the radical $\sqrt{4+\sqrt{4+\sqrt{4+\dots}}}$

Since $e=\sum_{n=0}^\infty\frac{1}{n!}=1+1+\frac12(1+\frac13(1+\frac14(1+\dots)))$

We have $4^{e-2}=\sqrt{4\cdot\sqrt[3]{4\cdot\sqrt[4]{4\cdots}}}$

Is there however a nice way to express the radical in the title too?

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