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%I #16 Sep 07 2015 14:27:06
%S 1,1,1,3,6,60,120,1260,6720,90720,362880,9979200,39916800,1037836800,
%T 10897286400,163459296000,1307674368000,59281238016000,
%U 355687428096000,15205637551104000,202741834014720000,5109094217170944000,51090942171709440000
%N Number of labeled cyclic groups with a fixed identity.
%C Degree of Lagrange resolvent of polynomial of n-th degree. Equals degree of symmetric group of order n divided by order of metacyclic group of order n. - _Artur Jasinski_, Jan 22 2008
%D J. L. Lagrange, Oeuvres, Vol. III Paris 1869.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = (n-1)!/phi(n).
%F a(n) = n!/A002618(n) - _Artur Jasinski_, Jan 22 2008
%e a(4)=3 because we have: <(1234)> = <(1432)>, <(1243)> = <(1342)>, <(1324)> = <(1423)>. - _Geoffrey Critzer_, Sep 07 2015
%t Table[n!/(n EulerPhi[n]), {n, 1, 20}] (* _Artur Jasinski_, Jan 22 2008 *)
%Y a(n) = A000142(n-1)/A000010(n) = A034381(n)/n.
%Y Cf. A058162, A058163.
%Y Cf. A002618.
%K nonn
%O 1,4
%A _Christian G. Bower_, Nov 14 2000
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