A054919 Number of nonisomorphic connected unlabeled binary relations on n nodes.

1, 2, 7, 86, 2818, 285382, 96324549, 112087100482, 458071928280897, 6665704296529088252, 349377209492194571020053, 66602723163954144515240479674, 46557323273646194397778583902876038, 120168498151800396724425973133360413846262, 1152049915423012273792614840793828654424980146983

Offset

0,2

Links

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

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Formula

Inverse Euler transform of A000595.

Example

Nonisomorphic connected relations on set {1,2} are {2r1}, {1r1,2r1}, {2r1,2r2}, {1r1,2r1,2r2}, {1r2,2r1}, {1r1,1r2,2r1}, {1r1,1r2,2r1,2r2} so a(2)=7.

Mathematica

nn=7; c=Join[{1, 2}, Table[CycleIndex[Join[PairGroup[SymmetricGroup[n], Ordered], Permutations[Range[n^2-n+1, n^2]], 2], s] /. Table[s[i]->2, {i, 1, n^2-n}], {n, 2, nn}]]; f[x_]:=Sum[a[n]x^n, {n, 0, nn}]; b=Sum[c[[n+1]]x^n, {n, 0, nn}]; sol=SolveAlways[b==Normal[Series[Product[1/(1-x^i)^a[i], {i, 1, nn}], {x, 0, nn}]], x]; Table[a[n], {n, 1, nn}]/.sol (* Geoffrey Critzer, Mar 31 2013 *)

Crossrefs

Cf. A000595.

Sequence in context: A268299 A041291 A209331 * A119157 A079701 A327039

Adjacent sequences: A054916 A054917 A054918 * A054920 A054921 A054922

Keyword

nonn,easy

Author

N. J. A. Sloane, May 24 2000

Extensions

More terms from Vladeta Jovovic, Jul 16 2000

a(0)=1 prepended and a(13)-a(14) from Andrew Howroyd, Sep 10 2018

Status

approved