A198085 Number of nonempty connected, containment-free subsets of 2^[n]. Total number of clutters on all subsets of [n]. Number of connected antichains in the Boolean algebra B_n (the poset of subsets of [n] ordered by containment).

1, 3, 11, 114, 6833, 7783197, 2414627236077, 56130437209370100252470

Offset: 1

Author

Gus Wiseman, Oct 21 2011

Keywords

• nonn
• more

Comments

The restriction to (spanning hypergraphs = maximal antichains = clutters on [n]) is considered in A048143.

Examples

			For n=3: {{1}}, {{2}}, {{3}}, {{12}}, {{13}}, {{23}}, {{123}}, {{12}{13}}, {{12}{23}}, {{13}{23}}, {{12}{13}{23}}.
		

Crossrefs

Cf. A048143.

Formula

a(n) = Sum_{k=1..n} binomial(n,k) * A048143(k). - Andrew Howroyd, Feb 04 2021

Extensions

a(6)-a(8) from Andrew Howroyd, Feb 04 2021