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Define a sequence of functions $\{f_n(x)\}$ as follows: $f_1(x) = 1, \hspace{.4cm} f_{n+1}(x) = \int_0^{\infty}\frac{e^{-tx}}{f_n(t)}dt.$ Evaluate: $\frac{f_{20}(1)f_{21}(1)}{f_{18}(1)f_{19}(1)}$

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