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 A324171 Number of non-crossing multiset partitions of normal multisets of size n. 14
 1, 1, 4, 16, 75, 378, 2042, 11489, 66697 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A multiset is normal if its union is an initial interval of positive integers. A multiset partition is crossing if it has a 2-element submultiset of the form {{...x...y...}, {...z...t...}} where x < z < y < t or z < x < t < y. LINKS EXAMPLE The A255906(5) - a(5) = 22 crossing multiset partitions:   {{13}{124}}  {{1}{13}{24}}   {{13}{224}}  {{1}{24}{35}}   {{13}{234}}  {{2}{13}{24}}   {{13}{244}}  {{2}{14}{35}}   {{13}{245}}  {{3}{13}{24}}   {{14}{235}}  {{3}{14}{25}}   {{24}{113}}  {{4}{13}{24}}   {{24}{123}}  {{4}{13}{25}}   {{24}{133}}  {{5}{13}{24}}   {{24}{134}}   {{24}{135}}   {{25}{134}}   {{35}{124}} MATHEMATICA nonXQ[stn_]:=!MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; xset[[x]])]&/@sps[Range[Length[set]]]]; allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; Table[Sum[Length[Select[mps[m], nonXQ]], {m, allnorm[n]}], {n, 0, 8}] CROSSREFS Cf. A000108 (non-crossing set partitions), A000124, A001006, A001055, A001263, A007297, A054726 (non-crossing graphs), A099947, A194560, A255906 (multiset partitions of normal multisets), A306438. Cf. A324166, A324167, A324168, A324169, A324170, A324173. Sequence in context: A331159 A101205 A301577 * A204772 A050540 A094559 Adjacent sequences:  A324168 A324169 A324170 * A324172 A324173 A324174 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 17 2019 STATUS approved

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Last modified January 28 14:26 EST 2022. Contains 350656 sequences. (Running on oeis4.)