A319155 - OEIS

%I #21 Oct 06 2019 17:47:00

%S 1,1,3,11,51,337,3500,60936,1866002,102768062,10296340496,

%T 1890236147880,639528747831552,400813006079742544,

%U 467517947968588109568,1019290779610824185400096,4170141472168738281510957264,32130367702064742239376997422512

%N Number of bicolored graphs on 2n unlabled nodes without isolated nodes and which are invariant when the two color classes are interchanged.

%H Andrew Howroyd, <a href="/A319155/b319155.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = A122082(n) - A122082(n-1).

%t permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];

%t edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total @ Quotient[v + 1, 2];

%t A122082[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/n!];

%t a[n_] := A122082[n] - A122082[n-1];

%t a /@ Range[0, 17] (* _Jean-François Alcover_, Sep 05 2019, after _Andrew Howroyd_ in A122082 *)

%Y Cf. A007140, A122082.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Sep 25 2018