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A317775 Number of strict multiset partitions of strongly normal multisets of size n, where a multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. 3
1, 3, 10, 36, 136, 596, 2656, 13187, 68226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

The a(3) = 10 strict multiset partitions:

  {{1,1,1}}, {{1},{1,1}},

  {{1,1,2}}, {{1},{1,2}}, {{2},{1,1}},

  {{1,2,3}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{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[Select[Join@@mps/@strnorm[n], UnsameQ@@#&]], {n, 6}]

CROSSREFS

Cf. A001055, A007716, A045778, A281116, A317449, A317584, A317654, A317755, A317757, A317776.

Sequence in context: A026854 A136576 A129156 * A171753 A002212 A149041

Adjacent sequences:  A317772 A317773 A317774 * A317776 A317777 A317778

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2018

STATUS

approved

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Last modified May 21 09:15 EDT 2019. Contains 323441 sequences. (Running on oeis4.)