A048143 Number of labeled connected simplicial complexes with n nodes.

1, 1, 1, 5, 84, 6348, 7743728, 2414572893530, 56130437190053299918162

Offset

0,4

Comments

Also number of connected antichains on a labeled n-set.

Links

Table of n, a(n) for n=0..8.

Patrick De Causmaecker, Stefan De Wannemacker, On the number of antichains of sets in a finite universe, arXiv:1407.4288 [math.CO], 2014.

Greg Huber, Letters to N. J. A. Sloane, May 1983 [Annotated, corrected, scanned copy]

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Example

For n=3 we could have 2 edges (in 3 ways), 3 edges (1 way), or 3 edges and a triangle (1 way), so a(3)=5.
a(5) = 1+75+645+1655+2005+1345+485+115+20+2 = 6348.

Crossrefs

Cf. A094033, A094034, A094035, A094036, A094037.

Cf. A000666, A006126, A030019, A054921, A120338, A275307, A285572.

Sequence in context: A288163 A268880 A367192 * A216420 A137083 A198586

Adjacent sequences: A048140 A048141 A048142 * A048144 A048145 A048146

Keyword

nonn,nice,more

Author

Greg Huber, May 12 1983

Extensions

More terms from Vladeta Jovovic, Jun 17 2006

Entry revised by N. J. A. Sloane, Jul 27 2006

Status

approved