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 A324011 Number of set partitions of {1, ..., n} with no singletons or cyclical adjacencies (successive elements in the same block, where 1 is a successor of n). 12
 1, 0, 0, 0, 1, 0, 5, 14, 66, 307, 1554, 8415, 48530, 296582, 1913561, 12988776, 92467629, 688528288, 5349409512, 43270425827, 363680219762, 3170394634443, 28619600156344, 267129951788160, 2574517930001445, 25587989366964056, 261961602231869825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS These set partitions are fixed points under Callan's bijection phi on set partitions. LINKS David Callan, On conjugates for set partitions and integer compositions, arXiv:math/0508052 [math.CO], 2005. EXAMPLE The a(4) = 1, a(6) = 5, and a(7) = 14 set partitions:   {{13}{24}}  {{135}{246}}    {{13}{246}{57}}               {{13}{25}{46}}  {{13}{257}{46}}               {{14}{25}{36}}  {{135}{26}{47}}               {{14}{26}{35}}  {{135}{27}{46}}               {{15}{24}{36}}  {{136}{24}{57}}                               {{136}{25}{47}}                               {{14}{257}{36}}                               {{14}{26}{357}}                               {{146}{25}{37}}                               {{146}{27}{35}}                               {{15}{246}{37}}                               {{15}{247}{36}}                               {{16}{24}{357}}                               {{16}{247}{35}} MATHEMATICA Table[Select[sps[Range[n]], And[Count[#, {_}]==0, Total[If[First[#]==1&&Last[#]==n, 1, 0]+Count[Subtract@@@Partition[#, 2, 1], -1]&/@#]==0]&]//Length, {n, 0, 10}] CROSSREFS Cf. A000110, A000126, A000296 (singletons allowed, or adjacencies allowed), A001610, A124323, A169985, A261139, A324012, A324014, A324015. Sequence in context: A197661 A004030 A256413 * A194994 A166795 A128102 Adjacent sequences:  A324008 A324009 A324010 * A324012 A324013 A324014 KEYWORD nonn AUTHOR Gus Wiseman, Feb 12 2019 EXTENSIONS a(11)-a(26) from Alois P. Heinz, Feb 12 2019 STATUS approved

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Last modified June 16 02:14 EDT 2021. Contains 345055 sequences. (Running on oeis4.)