User blog comment:Nayuta Ito/Organic Chemistry Notation/@comment-1605058-20150101092046

An upper bound for this function is n^((a_1+a_2+...+a_n)(a_1+a_2+...+a_n-1)/2), because there are a_1+a_2+...+a_n atoms and (a_1+a_2+...+a_n)(a_1+a_2+...+a_n-1)/2 pairs of them. Every pair is connected at most by n-bond, which gives the bound.