Consider the sequence \( a_{1}, a_{2}, a_{3}, \ldots . \). such that \( a_{1}=1, a_{2}=2 \) and \( a_{n+2}=\frac{2}{a_{n+1}}+a_{n} \) for \( n=1,2,3, \ldots \)
If \( \left(\frac{a_{1}+\frac{1}{a_{2}}}{a_{3}}\right) \cdot\left(\frac{a_{2}+\frac{1}{a_{3}}}{a_{4}}\right) \cdot\left(\frac{a_{3}+\frac{1}{a_{4}}}{a_{5}}\right) \ldots . .\left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^{\alpha}\left({ }^{61} C_{31}\right) \), then \( \alpha \) is equal to :
