Combinatorial Maxima

For each positive integer n, let A\(_{n}\)=max{\(\binom{n}{r}|0 \leq r \leq n\)}. Then the number of elements in {1, 2, 3, ....., 20} for which \(1.9 \leq \frac{A_{n}}{A_{n-1}} \leq 2\)

Note:This question is a part of set KVPY 2014 SB

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