\[a_{2}\left(q\right)=4+\tfrac{5}{12}q^{2}-\tfrac{763}{13824}q^{4}+\tfrac{10\;02%
401}{796\;26240}q^{6}-\tfrac{16690\;68401}{45\;86471\;42400}q^{8}+\cdots,\]