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 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 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

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Last modified January 29 02:42 EST 2023. Contains 359915 sequences. (Running on oeis4.)