I am not sure that I got that right. For example when n = 2, which is the coefficient for .

Also a_1 and a_2 appear once, a_3 and a_4 appear twice, a_5 and a_6 appear three times, a_7 and a_8 appear four times, etc. I'm not quite sure how to fit that into the coefficients since the number of a_n terms for any given n increases every two terms.