A318564 - OEIS

A318564

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

1, 6, 36, 274, 2408, 24440, 279172, 3542798, 49354816, 747851112, 12231881948, 214593346534, 4016624367288, 79843503990710, 1678916979373760, 37215518578700028, 866953456654946948, 21167221410812128266, 540346299720320080828, 14390314687100383124540, 399023209689817997883900

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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..21.

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}]

PROG

(PARI) \\ See links in A339645 for combinatorial species functions.

seq(n)={my(A=symGroupSeries(n)); NormalLabelingsSeq(sExp(sExp(A))-1)} \\ Andrew Howroyd, Jan 01 2021

CROSSREFS

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

Sequence in context: A144892 A204210 A366436 * A259818 A330449 A346547

Adjacent sequences: A318561 A318562 A318563 * A318565 A318566 A318567

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 29 2018

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Jan 01 2021

STATUS

approved