login
Weighted sum of all cyclic subgroups of the Symmetric Group.
2

%I #10 Jul 03 2018 02:25:11

%S 1,3,10,43,231,1531,11068,89895,820543,8484871,95647476,1186289083,

%T 15648402355,221728356123,3354790995676,53999879550991,

%U 936289020367263,17163114699673615,328827078340587148,6630244432204704771,139769193881466850051,3092293682224076627683

%N Weighted sum of all cyclic subgroups of the Symmetric Group.

%C Sum of the orders of all cyclic subgroups of the Sym_n.

%C The identity permutation is counted for each subgroup, i.e. A051625(n) times.

%C Each permutation is counted several times according to its conjugacy class.

%F a(n) = Sum_{k=1..A000793(n)} k*A074881(n, k). - _Andrew Howroyd_, Jul 02 2018

%e a(4) = 1*1 + 2*3 + 2*6 + 3*4 + 4*3 = 1+6+12+12+12 = 43.

%Y Cf. A000793, A051625, A074881.

%K nonn,easy

%O 1,2

%A _Olivier GĂ©rard_, Apr 03 2012

%E a(9)-a(22) from _Andrew Howroyd_, Jul 02 2018