cp's OEIS Frontend

A306416 Number of ordered set partitions of {1, ..., n} with no singletons or cyclical adjacencies (successive elements in the same block, where 1 is a successor of n).

%I A306416 #10 Feb 14 2019 19:26:24
%S A306416 1,0,0,0,2,0,26,84,950,6000,62522,556116,6259598,69319848,874356338,
%T A306416 11384093196,161462123894,2397736692144,37994808171962,
%U A306416 631767062124564,11088109048500158,203828700127054008,3928762035148317314,79079452776283889820,1661265965479375937030,36332908076071038467520,826376466514358722894154
%N A306416 Number of ordered set partitions of {1, ..., n} with no singletons or cyclical adjacencies (successive elements in the same block, where 1 is a successor of n).
%H A306416 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 A306416 The a(4) = 2 ordered set partitions are: {{1,3},{2,4}}, {{2,4},{1,3}}.
%t A306416 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A306416 Table[Sum[Length[stn]!,{stn,Select[sps[Range[n]],And[Count[#,{_}]==0,Total[If[First[#]==1&&Last[#]==n,1,0]+Count[Subtract@@@Partition[#,2,1],-1]&/@#]==0]&]}],{n,0,10}]
%Y A306416 Cf. A000110, A000126, A000296, A000670, A001610, A032032 (adjacencies allowed), A052841 (singletons allowed), A124323, A169985, A306417, A324011 (orderless case), A324012, A324015.
%K A306416 nonn
%O A306416 0,5
%A A306416 _Gus Wiseman_, Feb 14 2019
%E A306416 a(12)-a(26) from _Alois P. Heinz_, Feb 14 2019