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A318565 Number of multiset partitions of multiset partitions of strongly normal multisets of size n. 16
1, 6, 27, 169, 1029, 7817, 61006, 547537 (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, and strongly normal if in addition it has weakly decreasing multiplicities.

LINKS

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

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]]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

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

CROSSREFS

Cf. A001970, A007716, A050336, A255906, A269134, A317533, A317791, A318564, A318566.

Sequence in context: A117336 A202766 A144013 * A092854 A223557 A289022

Adjacent sequences:  A318562 A318563 A318564 * A318566 A318567 A318568

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 29 2018

STATUS

approved

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Last modified November 12 07:00 EST 2019. Contains 329052 sequences. (Running on oeis4.)