some pep8, some code details, one shorter doctest, standard errors, etc

also using formatted strings a little bit

and modern syntax for super()

CC: @tscrim @kwankyu @dcoudert

Component: combinatorics

Author: Frédéric Chapoton

Branch/Commit: f1da83e

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/34622