login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318564 Number of multiset partitions of multiset partitions of normal multisets of size n. 16
1, 6, 36, 274, 2408, 24440, 279172, 3542798, 49354816, 747851112, 12231881948, 214593346534, 4016624367288, 79843503990710, 1678916979373760, 37215518578700028, 866953456654946948, 21167221410812128266, 540346299720320080828, 14390314687100383124540, 399023209689817997883900 (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
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
Sequence in context: A144892 A204210 A366436 * A259818 A330449 A346547
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 29 2018
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Jan 01 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)