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 A326335 Number of set partitions of {1..n} whose nesting blocks are connected. 5
 1, 1, 1, 1, 2, 6, 21, 86, 394, 1974, 10696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Two blocks are nesting if they are of the form {...x,y...}, {...z,t...} where x < z < t < y or z < x < y < t. A set partition has its nesting blocks connected if the graph whose vertices are the blocks and whose edges are nesting pairs of blocks is connected. LINKS Table of n, a(n) for n=0..10. EXAMPLE The a(0) = 1 through a(6) = 21 set partitions: {} {1} {12} {123} {1234} {12345} {123456} {14}{23} {125}{34} {1236}{45} {134}{25} {1245}{36} {14}{235} {125}{346} {145}{23} {1256}{34} {15}{234} {126}{345} {134}{256} {1345}{26} {1346}{25} {136}{245} {14}{2356} {145}{236} {1456}{23} {146}{235} {15}{2346} {156}{234} {16}{2345} {15}{26}{34} {16}{23}{45} {16}{24}{35} {16}{25}{34} MATHEMATICA nesXQ[stn_]:=MatchQ[stn, {___, {___, x_, y_, ___}, ___, {___, z_, t_, ___}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; nestcmpts[stn_]:=csm[Union[List/@stn, Select[Subsets[stn, {2}], nesXQ]]]; sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; Table[Length[Select[sps[Range[n]], Length[nestcmpts[#]]<=1&]], {n, 0, 5}] CROSSREFS Simple graphs whose nesting blocks are connected are A326330. Set partitions whose crossing blocks are connected are A099947. Set partitions whose capturing blocks are connected are A326336. Cf. A000110, A001519, A016098, A122880, A324173, A326243, A326248, A326293, A326331, A326337. Sequence in context: A344229 A090805 A150226 * A256180 A150227 A263852 Adjacent sequences: A326332 A326333 A326334 * A326336 A326337 A326338 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 27 2019 STATUS approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)