OFFSET
1,3
COMMENTS
A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.
EXAMPLE
The a(3) = 6 strongly normal multiset partitions with empty intersection:
{{2},{1,1}}
{{1},{2,3}}
{{2},{1,3}}
{{3},{1,2}}
{{1},{1},{2}}
{{1},{2},{3}}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];
Table[Length[Join@@Table[Select[mps[m], Intersection@@#=={}&], {m, strnorm[n]}]], {n, 6}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 06 2018
EXTENSIONS
a(10)-a(11) from Robert Price, May 08 2021
STATUS
approved