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

Author

Olivier Gérard, Apr 04 2012

Keywords

• nonn
• easy

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).

Examples

			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.

Formula

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