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A317757 Number of non-isomorphic multiset partitions of size n such that the blocks have empty intersection. 35

%I

%S 0,1,4,17,56,205,690,2446,8506,30429

%N Number of non-isomorphic multiset partitions of size n such that the blocks have empty intersection.

%e Non-isomorphic representatives of the a(4) = 17 multiset partitions:

%e {1}{234},{2}{111},{2}{113},{11}{22},{11}{23},{12}{34},

%e {1}{1}{22},{1}{1}{23},{1}{2}{11},{1}{2}{12},{1}{2}{13},{1}{2}{34},{2}{3}{11},

%e {1}{1}{1}{2},{1}{1}{2}{2},{1}{1}{2}{3},{1}{2}{3}{4}.

%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];

%t mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

%t strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];

%t sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]],sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]],i},{i,Length[Union@@m]}]],First[Sort[sysnorm[m,1]]]];sysnorm[m_,aft_]:=If[Length[Union@@m]<=aft,{m},With[{mx=Table[Count[m,i,{2}],{i,Select[Union@@m,#>=aft&]}]},Union@@(sysnorm[#,aft+1]&/@Union[Table[Map[Sort,m/.{par+aft-1->aft,aft->par+aft-1},{0,1}],{par,First/@Position[mx,Max[mx]]}]])]];

%t Table[Length[Union[sysnorm/@Join@@Table[Select[mps[m],Intersection@@#=={}&],{m,strnorm[n]}]]],{n,6}]

%Y Cf. A007716, A035310, A255906, A281116, A317073, A317533.

%Y Cf. A317748, A317751, A317752, A317755.

%Y Cf. A319077, A319748, A319755, A319778, A319781, A319790.

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Aug 06 2018

%E a(8) - a(10) from _Gus Wiseman_, Sep 27 2018

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Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)