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 A326246 Number of crossing, capturing set partitions of {1..n}. 9
 0, 0, 0, 0, 0, 3, 37, 307, 2173, 14344, 92402, 596688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A set partition is crossing if it has two blocks of the form {...x...y...}, {...z...t...} where x < z < y < t or z < x < t < y, and capturing if it has two blocks of the form {...x...y...}, {...z...t...} where x < z < t < y or z < x < y < t. Capturing is a weaker condition than nesting, so for example {{1,3,5},{2,4}} is capturing but not nesting. LINKS Eric Marberg, Crossings and nestings in colored set partitions, arXiv preprint arXiv:1203.5738 [math.CO], 2012. EXAMPLE The a(5) = 3 set partitions:   {{1,3,4},{2,5}}   {{1,3,5},{2,4}}   {{1,4},{2,3,5}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified July 24 21:47 EDT 2021. Contains 346273 sequences. (Running on oeis4.)