

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

Table of n, a(n) for n=1..5.
Sebastian Bozlee, Bob Kuo, and Adrian Neff, A classification of modular compactifications of the space of pointed elliptic curves by Gorenstein curves, arXiv:2105.10582 [math.AG], 2021.


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

Equals A302250  1, Cf. A000372, A007153, A003182, A014466.
Sequence in context: A005271 A258668 A012938 * A013093 A013169 A012991
Adjacent sequences: A302248 A302249 A302250 * A302252 A302253 A302254


KEYWORD

nonn,hard,more


AUTHOR

John Machacek, Apr 04 2018


STATUS

approved



