A318566 Number of non-isomorphic multiset partitions of multiset partitions of multisets of size n.

1, 6, 21, 104, 452, 2335, 11992, 66810, 385101, 2336352, 14738380, 96831730, 659809115, 4657075074, 33974259046, 255781455848, 1984239830571, 15839628564349, 129951186405574, 1094486382191624, 9453318070371926, 83654146992936350, 757769011659766015, 7020652591448497490

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Example

Non-isomorphic representatives of the a(3) = 21 multiset partitions of multiset partitions:
  {{{1,1,1}}}
  {{{1,1,2}}}
  {{{1,2,3}}}
  {{{1},{1,1}}}
  {{{1},{1,2}}}
  {{{1},{2,3}}}
  {{{2},{1,1}}}
  {{{1},{1},{1}}}
  {{{1},{1},{2}}}
  {{{1},{2},{3}}}
  {{{1}},{{1,1}}}
  {{{1}},{{1,2}}}
  {{{1}},{{2,3}}}
  {{{2}},{{1,1}}}
  {{{1}},{{1},{1}}}
  {{{1}},{{1},{2}}}
  {{{1}},{{2},{3}}}
  {{{2}},{{1},{1}}}
  {{{1}},{{1}},{{1}}}
  {{{1}},{{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];
dubnorm[m_]:=First[Union[Table[Map[Sort, m/.Rule@@@Table[{Union[Flatten[m]][[i]], Union[Flatten[m]][[perm[[i]]]]}, {i, Length[perm]}], {0, 2}], {perm, Permutations[Union[Flatten[m]]]}]]];
Table[Length[Union[dubnorm/@Join@@mps/@Join@@mps/@strnorm[n]]], {n, 5}]

Prog

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

Crossrefs

Cf. A001970, A007716, A050336, A050338, A255906, A269134, A317533, A317791, A318564, A318565.

Sequence in context: A012662 A012418 A203295 * A083558 A060843 A026650

Adjacent sequences: A318563 A318564 A318565 * A318567 A318568 A318569

Keyword

nonn

Author

Gus Wiseman, Aug 29 2018

Extensions

Terms a(8) and beyond from Andrew Howroyd, Dec 30 2020

Status

approved