The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A302251 The number of nonempty antichains in the lattice of set partitions. 1
 1, 2, 9, 346, 79814831 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 06:02 EST 2023. Contains 367685 sequences. (Running on oeis4.)