

A302251


The number of nonempty antichains in the lattice of set partitions.


1




OFFSET

1,2


COMMENTS

Computing terms in this sequence is analogous to Dedekind's problem which asks for the number of antichains in the Boolean algebra.
This count excludes the empty antichain consisting of no set partitions.


LINKS



EXAMPLE

For n = 3 the a(3) = 9 nonempty antichains are:
{1/2/3}
{1/23}
{12/3}
{13/2}
{1/23, 12/3}
{1/23, 13/2}
{12/3, 13/2}
{1/23, 12/3, 13/2}
{123}
Here we have used the usual shorthand notation for set partitions where 1/23 denotes {{1}, {2,3}}.


PROG

(Sage)
[Posets.SetPartitions(n).antichains().cardinality()  1 for n in range(4)]
# minus removes the empty antichain


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



