A181964 Sum of the sizes of normalizers of all the cyclic subgroups of Alternating Group of order n.

1, 1, 6, 36, 240, 2160, 20160, 241920, 2903040, 39916800, 578793600, 9580032000, 161902540800, 3007651046400, 58845346560000, 1234444603392000, 26854400821248000, 624231436308480000, 15083992450695168000, 385614968295997440000

Offset

1,3

Comments

For each cyclic subgroup of the Alternate group on n symbols, add the size of its normalizer (permutations leaving the subgroup invariant by conjugation).

a(7) is remarquable because it is equal to the size of Alt(8).

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = n!/2 * A046682(n).

Example

Decomposing by number of cyclic subgroups * size of normalizer of subgroups
a(5) = 1*60 + 4*15 + 6*10 + 0*60 + 10*6 = 240.
a(6) = 1*360 + 8*45 + (18*20+18*20) + 8*45 + 10*36 = 2160.

Crossrefs

Cf. A053529, A181950.

Sequence in context: A153824 A001286 A180119 * A354457 A199422 A049431

Adjacent sequences: A181961 A181962 A181963 * A181965 A181966 A181967

Keyword

nonn,easy

Author

Olivier Gérard, Apr 04 2012

Status

approved