A199574 The number of simple labeled graphs on n nodes where two such graphs are considered equivalent iff one can be obtained from the other by reversing the labeling.

1, 2, 6, 40, 544, 16640, 1050624, 134250496, 34360262656, 17592202821632, 18014399046352896, 36893488181778841600, 151115727454027670093824, 1237940039285661749875834880, 20282409603651706452744270249984

Offset: 1

Author

Geoffrey Critzer, Nov 09 2011

Keywords

• nonn

Comments

Equivalently, The number of orbits in the set of simple labeled graphs on n nodes under the action of the permutation group G = {{1,2,...,n},{n,n-1,...,1}}.

The induced group has cycle index= 1/2(s_1^binomial(n,2)+s_1^floor(n/2)s_2^((binomial(n,2)-floor(n/2))/2))

Examples

			a(3)=6 because:1-2 3 is equivalent to 1 2-3 and 3-1-2 is equivalent to 1-3-2 while the other four graphs are fixed for a total of 6 orbits.
		

Programs

Mathematica

Table[PairGroupIndex[{e=IdentityPermutation[n],Reverse[e]},s]/.Table[s[i]->2,{i,1,2}],{n,1,20}]

Formula

a(n)= (2^floor(n/2)+2^((binomial(n,2)+floor(n/2)/2))/2