A319155 Number of bicolored graphs on 2n unlabled nodes without isolated nodes and which are invariant when the two color classes are interchanged.

1, 1, 3, 11, 51, 337, 3500, 60936, 1866002, 102768062, 10296340496, 1890236147880, 639528747831552, 400813006079742544, 467517947968588109568, 1019290779610824185400096, 4170141472168738281510957264, 32130367702064742239376997422512

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

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

Mathematica

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];
edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total @ Quotient[v + 1, 2];
A122082[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/n!];
a[n_] := A122082[n] - A122082[n-1];
a /@ Range[0, 17] (* Jean-François Alcover, Sep 05 2019, after Andrew Howroyd in A122082 *)

Crossrefs

Cf. A007140, A122082.

Sequence in context: A182176 A244754 A129097 * A362468 A292927 A367046

Adjacent sequences: A319152 A319153 A319154 * A319156 A319157 A319158

Keyword

nonn

Author

Andrew Howroyd, Sep 25 2018

Status

approved