cp's OEIS Frontend

A324171 Number of non-crossing multiset partitions of normal multisets of size n.

%I A324171 #7 Feb 19 2019 00:08:17
%S A324171 1,1,4,16,75,378,2042,11489,66697
%N A324171 Number of non-crossing multiset partitions of normal multisets of size n.
%C A324171 A multiset is normal if its union is an initial interval of positive integers.
%C A324171 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.
%e A324171 The A255906(5) - a(5) = 22 crossing multiset partitions:
%e A324171   {{13}{124}}  {{1}{13}{24}}
%e A324171   {{13}{224}}  {{1}{24}{35}}
%e A324171   {{13}{234}}  {{2}{13}{24}}
%e A324171   {{13}{244}}  {{2}{14}{35}}
%e A324171   {{13}{245}}  {{3}{13}{24}}
%e A324171   {{14}{235}}  {{3}{14}{25}}
%e A324171   {{24}{113}}  {{4}{13}{24}}
%e A324171   {{24}{123}}  {{4}{13}{25}}
%e A324171   {{24}{133}}  {{5}{13}{24}}
%e A324171   {{24}{134}}
%e A324171   {{24}{135}}
%e A324171   {{25}{134}}
%e A324171   {{35}{124}}
%t A324171 nonXQ[stn_]:=!MatchQ[stn,{___,{___,x_,___,y_,___},___,{___,z_,___,t_,___},___}/;x<z<y<t||z<x<t<y];
%t A324171 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A324171 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A324171 allnorm[n_]:=If[n<=0,{{}},Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]];
%t A324171 Table[Sum[Length[Select[mps[m],nonXQ]],{m,allnorm[n]}],{n,0,8}]
%Y A324171 Cf. A000108 (non-crossing set partitions), A000124, A001006, A001055, A001263, A007297, A054726 (non-crossing graphs), A099947, A194560, A255906 (multiset partitions of normal multisets), A306438.
%Y A324171 Cf. A324166, A324167, A324168, A324169, A324170, A324173.
%K A324171 nonn,more
%O A324171 0,3
%A A324171 _Gus Wiseman_, Feb 17 2019