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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). 2
1, 0, 0, 0, 2, 0, 26, 84, 950, 6000, 62522, 556116, 6259598, 69319848, 874356338, 11384093196, 161462123894, 2397736692144, 37994808171962, 631767062124564, 11088109048500158, 203828700127054008, 3928762035148317314, 79079452776283889820, 1661265965479375937030, 36332908076071038467520, 826376466514358722894154 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..26.

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

Cf. A000110, A000126, A000296, A000670, A001610, A032032 (adjacencies allowed), A052841 (singletons allowed), A124323, A169985, A306417, A324011 (orderless case), A324012, A324015.

Sequence in context: A158045 A157304 A157305 * A156459 A007218 A092177

Adjacent sequences:  A306413 A306414 A306415 * A306417 A306418 A306419

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 14 2019

EXTENSIONS

a(12)-a(26) from Alois P. Heinz, Feb 14 2019

STATUS

approved

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Last modified July 22 14:31 EDT 2019. Contains 325222 sequences. (Running on oeis4.)