A048143 Number of labeled connected simplicial complexes with n nodes.

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

Offset: 0

Author

Greg Huber, May 12 1983

Keywords

• nonn
• nice
• more

Comments

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

Examples

			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.
		

Links

• 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.

Crossrefs

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

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

Extensions

More terms from Vladeta Jovovic, Jun 17 2006

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