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A317584 Number of multiset partitions of strongly normal multisets of size n such that all blocks have the same size. 3

%I

%S 1,4,6,19,14,113,30,584

%N Number of multiset partitions of strongly normal multisets of size n such that all blocks have the same size.

%C A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.

%e The a(4) = 19 multiset partitions:

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

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

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

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

%e {{1,2,3,4}}, {{1,2},{3,4}}, {{1,3},{2,4}}, {{1,4},{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 Table[Length[Select[Join@@mps/@strnorm[n],SameQ@@Length/@#&]],{n,6}]

%Y Cf. A000005, A007716, A038041, A255906, A298422, A306017, A306018, A306019, A306020, A306021, A317583.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Aug 01 2018

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Last modified August 24 16:39 EDT 2019. Contains 326295 sequences. (Running on oeis4.)