Closed form for $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$

limits nested-radicals

Given the fact that neither Somos' quadratic recurrence constant, nor the nested radical constant are known to possess a closed form, I find it highly doubtful that this one will fare any better... Same as to the nature of the number, given that the nature of the afore-mentioned two constants is also unknown.

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