This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324014 #5 Feb 12 2019 22:36:24
%S A324014 1,0,1,1,2,3,9,16,43,89,250,571,1639
%N A324014 Number of self-complementary set partitions of {1, ..., n} with no cyclical adjacencies (successive elements in the same block, where 1 is a successor of n).
%C A324014 The complement of a set partition pi of {1, ..., n} is defined as n + 1 - pi (elementwise) on page 3 of Callan. For example, the complement of {{1,5},{2},{3,6},{4}} is {{1,4},{2,6},{3},{5}}.
%H A324014 David Callan, <a href="https://arxiv.org/abs/math/0508052">On conjugates for set partitions and integer compositions</a> [math.CO].
%e A324014 The a(3) = 1 through a(6) = 9 self-complementary set partitions with no cyclical adjacencies:
%e A324014 {{1}{2}{3}} {{13}{24}} {{14}{25}{3}} {{135}{246}}
%e A324014 {{1}{2}{3}{4}} {{1}{24}{3}{5}} {{13}{25}{46}}
%e A324014 {{1}{2}{3}{4}{5}} {{14}{25}{36}}
%e A324014 {{1}{24}{35}{6}}
%e A324014 {{13}{2}{46}{5}}
%e A324014 {{14}{2}{36}{5}}
%e A324014 {{15}{26}{3}{4}}
%e A324014 {{1}{25}{3}{4}{6}}
%e A324014 {{1}{2}{3}{4}{5}{6}}
%t A324014 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A324014 cmp[stn_]:=Union[Sort[Max@@Join@@stn+1-#]&/@stn];
%t A324014 Table[Select[sps[Range[n]],And[cmp[#]==Sort[#],Total[If[First[#]==1&&Last[#]==n,1,0]+Count[Subtract@@@Partition[#,2,1],-1]&/@#]==0]&]//Length,{n,0,10}]
%Y A324014 Cf. A000110, A000296, A001610, A080107 (self-complementary), A169985, A324012 (self-conjugate), A324015.
%K A324014 nonn,more
%O A324014 0,5
%A A324014 _Gus Wiseman_, Feb 12 2019