If \( A_{r} \) is the coefficient of \( x^{r} \) in the expansion of \[ (1+x)^{2}\left(1+\frac{x...
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0If \( A_{r} \) is the coefficient of \( x^{r} \) in the expansion of
\[
(1+x)^{2}\left(1+\frac{x}{2}\right)^{2}\left(1+\frac{x}{2^{2}}\right)^{2}\left(1+\frac{x}{2^{3}}\right)^{2} \cdots
\]
prove that \( A_{r}=\frac{2^{2}}{2^{r}-1}\left(A_{r-1}+A_{r-2}\right) \), and \( A_{4}=\frac{1072}{315} \)
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