login
A319155
Number of bicolored graphs on 2n unlabled nodes without isolated nodes and which are invariant when the two color classes are interchanged.
2
1, 1, 3, 11, 51, 337, 3500, 60936, 1866002, 102768062, 10296340496, 1890236147880, 639528747831552, 400813006079742544, 467517947968588109568, 1019290779610824185400096, 4170141472168738281510957264, 32130367702064742239376997422512
OFFSET
0,3
LINKS
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
Sequence in context: A182176 A244754 A129097 * A362468 A292927 A367046
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Sep 25 2018
STATUS
approved