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%I #10 May 09 2021 02:47:46
%S 0,1,6,30,130,629,2930,15019,78224,438626,2548481
%N Number of multiset partitions of strongly normal multisets of size n such that the blocks have empty intersection.
%C A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.
%e The a(3) = 6 strongly normal multiset partitions with empty intersection:
%e {{2},{1,1}}
%e {{1},{2,3}}
%e {{2},{1,3}}
%e {{3},{1,2}}
%e {{1},{1},{2}}
%e {{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 strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
%t Table[Length[Join@@Table[Select[mps[m],Intersection@@#=={}&],{m,strnorm[n]}]],{n,6}]
%Y Cf. A007716, A035310, A255906, A317073, A281116, A317077, A317078, A317532, A317533.
%Y Cf. A317748, A317751, A317752, A317757, A317775.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Aug 06 2018
%E a(10)-a(11) from _Robert Price_, May 08 2021
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