Expansion of e.g.f. theta_3^(15/2).

Terms

a(0) =1a(1) =15a(2) =195a(3) =2145a(4) =19665a(5) =158535a(6) =1447875a(7) =18243225a(8) =232985025a(9) =2435846175a(10) =28443399075a(11) =508347464625