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 A317755 Number of multiset partitions of strongly normal multisets of size n such that the blocks have empty intersection. 22
 0, 1, 6, 30, 130, 629, 2930, 15019, 78224, 438626, 2548481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. LINKS 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 Cf. A007716, A035310, A255906, A317073, A281116, A317077, A317078, A317532, A317533. Cf. A317748, A317751, A317752, A317757, A317775. Sequence in context: A320744 A232061 A247386 * A036068 A162743 A224290 Adjacent sequences:  A317752 A317753 A317754 * A317756 A317757 A317758 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 06 2018 EXTENSIONS a(10)-a(11) from Robert Price, May 08 2021 STATUS approved

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Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)