A318565 Number of multiset partitions of multiset partitions of strongly normal multisets of size n.

1, 6, 27, 169, 1029, 7817, 61006, 547537, 5202009, 54506262, 606311524, 7299051826, 92985064466, 1264720212352, 18137495642192, 275078184766323, 4379514178076452, 73235806332442156, 1280229713195027792, 23381809052104639236, 444740694108284116235, 8801030741502964613534

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..22.

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}]

Prog

(PARI) \\ See links in A339645 for combinatorial species functions.
seq(n)={my(A=symGroupSeries(n)); StronglyNormalLabelingsSeq(sExp(sExp(A))-1)} \\ Andrew Howroyd, Dec 30 2020

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

Author

Gus Wiseman, Aug 29 2018

Extensions

Terms a(9) and beyond from Andrew Howroyd, Dec 30 2020

Status

approved