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A318564 Number of multiset partitions of multiset partitions of normal multisets of size n. 14
1, 6, 36, 274, 2408, 24440, 279172 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

The a(2) = 6 multiset partitions of multiset partitions:

  {{{1,1}}}

  {{{1,2}}}

  {{{1},{1}}}

  {{{1},{2}}}

  {{{1}},{{1}}}

  {{{1}},{{2}}}

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_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]];

Table[Sum[Length[mps[m]], {m, Join@@mps/@allnorm[n]}], {n, 6}]

CROSSREFS

Cf. A001970, A007716, A050336, A255906, A269134, A317533, A317791, A318566.

Sequence in context: A299330 A144892 A204210 * A259818 A134008 A125795

Adjacent sequences:  A318561 A318562 A318563 * A318565 A318566 A318567

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 29 2018

STATUS

approved

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Last modified November 19 03:40 EST 2019. Contains 329310 sequences. (Running on oeis4.)