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A317752 Number of multiset partitions of normal multisets of size n such that the blocks have empty intersection. 19
0, 1, 8, 49, 305, 1984, 13686, 100124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A multiset is normal if it spans an initial interval of positive integers.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

The a(3) = 8 multiset partitions with empty intersection:

  {{2},{1,1}}

  {{1},{2,2}}

  {{1},{2,3}}

  {{2},{1,3}}

  {{3},{1,2}}

  {{1},{1},{2}}

  {{1},{2},{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]]]];

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

Table[Length[Join@@Table[Select[mps[m], Intersection@@#=={}&], {m, allnorm[n]}]], {n, 6}]

CROSSREFS

Cf. A007716, A255903, A255906, A317073, A281116, A317077, A317532, A317533.

Cf. A317748, A317751, A317755, A317757, A317776.

Sequence in context: A037539 A037483 A188708 * A273497 A024106 A176626

Adjacent sequences:  A317749 A317750 A317751 * A317753 A317754 A317755

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2018

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)