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 A326249 Number of capturing set partitions of {1..n} that are not nesting. 9
 0, 0, 0, 0, 0, 1, 9, 55, 283, 1324, 5838, 24744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Capturing is a weaker condition than nesting. A set partition is capturing if it has two blocks of the form {...x...y...}, {...z...t...} where x < z < t < y or z < x < y < t, and nesting if it has two blocks of the form {...x,y...}, {...z,t...} where x < z < t < y or z < x < y < t. For example, {{1,3,5},{2,4}} is capturing but not nesting, so is counted under a(5). LINKS EXAMPLE The a(6) = 9 set partitions:   {{1},{2,4,6},{3,5}}   {{1,3,5},{2,4},{6}}   {{1,3,6},{2,4},{5}}   {{1,3,6},{2,5},{4}}   {{1,4,6},{2},{3,5}}   {{1,4,6},{2,5},{3}}   {{1,3,5},{2,4,6}}   {{1,2,4,6},{3,5}}   {{1,3,5,6},{2,4}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; capXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)