cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A199574 #20 Mar 30 2012 17:23:11
%S A199574 1,2,6,40,544,16640,1050624,134250496,34360262656,17592202821632,
%T A199574 18014399046352896,36893488181778841600,151115727454027670093824,
%U A199574 1237940039285661749875834880,20282409603651706452744270249984
%N 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.
%C A199574 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}}.
%C A199574 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))
%F A199574 a(n)= (2^floor(n/2)+2^((binomial(n,2)+floor(n/2)/2))/2
%e A199574 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.
%t A199574 Table[PairGroupIndex[{e=IdentityPermutation[n],Reverse[e]},s]/.Table[s[i]->2,{i,1,2}],{n,1,20}]
%K A199574 nonn
%O A199574 1,2
%A A199574 _Geoffrey Critzer_, Nov 09 2011