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%I #11 Nov 27 2024 12:33:13
%S 0,0,0,0,1,12,84,560,3276,79632,1105104,16571808,176344740
%N Number of subgroups of S_n isomorphic to S_5, where S_n is the n-th symmetric group.
%o (GAP) A378281 := function(n)
%o local S;
%o S := SymmetricGroup(n);
%o return Sum(IsomorphicSubgroups(S, SymmetricGroup(5)), x->Index(S, Normalizer(S, Image(x))));
%o end;
%Y Column k=5 of A378163.
%Y Cf. A000085, A378279, A378280.
%K nonn,hard,more
%O 1,6
%A _Jianing Song_, Nov 21 2024