Consider the sequence \( a_1, a_2, a_3, \ldots \) such that \( a_1 = 1, a_2 = 2 \) and \( a_{n+2} = \dfrac{2}{a_{n+1}} + a_n \) for \( n = 1, 2, 3, \ldots \). If
\( \left( \dfrac{a_1 + \dfrac{1}{a_2}}{a_3} \right)\left( \dfrac{a_2 + \dfrac{1}{a_3}}{a_4} \right)\left( \dfrac{a_3 + \dfrac{1}{a_4}}{a_5} \right) \ldots \left( \dfrac{a_{30} + \dfrac{1}{a_{31}}}{a_{32}} \right) = 2^{\alpha}\left( {}^{61}C_{31} \right) \) , then \( \alpha \) is equal to:
