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A317776 Number of strict multiset partitions of normal multisets of size n, where a multiset is normal if it spans an initial interval of positive integers. 6

%I

%S 1,3,13,59,313,1847,11977

%N Number of strict multiset partitions of normal multisets of size n, where a multiset is normal if it spans an initial interval of positive integers.

%e The a(3) = 13 strict multiset partitions:

%e {{1,1,1}}, {{1},{1,1}},

%e {{1,2,2}}, {{1},{2,2}}, {{2},{1,2}},

%e {{1,1,2}}, {{1},{1,2}}, {{2},{1,1}},

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

%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 allnorm[n_Integer]:=Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];

%t Table[Length[Select[Join@@mps/@allnorm[n],UnsameQ@@#&]],{n,9}]

%Y Cf. A001055, A007716, A045778, A255906, A281116, A317449, A317532, A317583, A317653, A317752, A317757, A317775.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Aug 06 2018

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Last modified May 24 01:29 EDT 2019. Contains 323528 sequences. (Running on oeis4.)