A181949 Weighted sum of all cyclic subgroups of the Symmetric Group.

1, 3, 10, 43, 231, 1531, 11068, 89895, 820543, 8484871, 95647476, 1186289083, 15648402355, 221728356123, 3354790995676, 53999879550991, 936289020367263, 17163114699673615, 328827078340587148, 6630244432204704771, 139769193881466850051, 3092293682224076627683

Offset

1,2

Comments

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

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

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

Links

Table of n, a(n) for n=1..22.

Formula

a(n) = Sum_{k=1..A000793(n)} k*A074881(n, k). - Andrew Howroyd, Jul 02 2018

Example

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

Crossrefs

Cf. A000793, A051625, A074881.

Sequence in context: A248687 A006932 A001040 * A162286 A032269 A179501

Adjacent sequences: A181946 A181947 A181948 * A181950 A181951 A181952

Keyword

nonn,easy

Author

Olivier Gérard, Apr 03 2012

Extensions

a(9)-a(22) from Andrew Howroyd, Jul 02 2018

Status

approved