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%I #11 Feb 13 2019 03:30:32
%S 1,0,0,0,1,0,5,14,66,307,1554,8415,48530,296582,1913561,12988776,
%T 92467629,688528288,5349409512,43270425827,363680219762,3170394634443,
%U 28619600156344,267129951788160,2574517930001445,25587989366964056,261961602231869825
%N 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).
%C These set partitions are fixed points under Callan's bijection phi on set partitions.
%H David Callan, <a href="https://arxiv.org/abs/math/0508052">On conjugates for set partitions and integer compositions</a>, arXiv:math/0508052 [math.CO], 2005.
%e The a(4) = 1, a(6) = 5, and a(7) = 14 set partitions:
%e {{13}{24}} {{135}{246}} {{13}{246}{57}}
%e {{13}{25}{46}} {{13}{257}{46}}
%e {{14}{25}{36}} {{135}{26}{47}}
%e {{14}{26}{35}} {{135}{27}{46}}
%e {{15}{24}{36}} {{136}{24}{57}}
%e {{136}{25}{47}}
%e {{14}{257}{36}}
%e {{14}{26}{357}}
%e {{146}{25}{37}}
%e {{146}{27}{35}}
%e {{15}{246}{37}}
%e {{15}{247}{36}}
%e {{16}{24}{357}}
%e {{16}{247}{35}}
%t 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}]
%Y Cf. A000110, A000126, A000296 (singletons allowed, or adjacencies allowed), A001610, A124323, A169985, A261139, A324012, A324014, A324015.
%K nonn
%O 0,7
%A _Gus Wiseman_, Feb 12 2019
%E a(11)-a(26) from _Alois P. Heinz_, Feb 12 2019
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