OFFSET
0,5
LINKS
David Callan, On conjugates for set partitions and integer compositions, arXiv:math/0508052 [math.CO], 2005.
EXAMPLE
The a(4) = 2 ordered set partitions are: {{1,3},{2,4}}, {{2,4},{1,3}}.
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 14 2019
EXTENSIONS
a(12)-a(26) from Alois P. Heinz, Feb 14 2019
STATUS
approved