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A302251
The number of nonempty antichains in the lattice of set partitions.
1
1, 2, 9, 346, 79814831
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.
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
KEYWORD
nonn,hard,more
AUTHOR
John Machacek, Apr 04 2018
STATUS
approved