

A198085


Number of nonempty connected, containmentfree 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).


8




OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..8.


FORMULA

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


EXAMPLE

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


CROSSREFS

Cf. A048143.
Sequence in context: A275338 A068693 A036930 * A319749 A209107 A015047
Adjacent sequences: A198082 A198083 A198084 * A198086 A198087 A198088


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Oct 21 2011


EXTENSIONS

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


STATUS

approved



