The Nottingham group at 2 is the of (formal) power series t+a2t2+a3t3+⋯ in variable t with coefficients ai from field two elements, where operation given by composition series. depth such a largest d⩾1 for which a2=…=ad=0. Only handful finite order (forcedly 2) are explicitly known through formula their coefficients. We argue this paper that it advantageous to describe closed computational form...