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%I #18 Jan 28 2023 11:58:14
%S 1,1,7,9,35,48,135
%N a(n) = number of regular polytopes of rank m-n with group S_m, up to isomorphism and duality (this is independent of m if m >= 2n+3).
%C Also known as string C-groups for S_m.
%H Peter J. Cameron, Maria Elisa Fernandes and Dimitri Leemans, <a href="https://arxiv.org/abs/2212.12723">The number of string C-groups of high rank</a>, arXiv:2212.12723 [math.GR], 2022.
%e a(1)=1 since the only regular polytope of rank m-1 with group S_m is the simplex.
%K nonn,hard,more
%O 1,3
%A _Peter J. Cameron_, Dec 28 2022
%E a(7) from _Peter J. Cameron_, Jan 19 2023