cp's OEIS Frontend

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

%I A318566 #8 Dec 30 2020 17:11:24
%S A318566 1,6,21,104,452,2335,11992,66810,385101,2336352,14738380,96831730,
%T A318566 659809115,4657075074,33974259046,255781455848,1984239830571,
%U A318566 15839628564349,129951186405574,1094486382191624,9453318070371926,83654146992936350,757769011659766015,7020652591448497490
%N A318566 Number of non-isomorphic multiset partitions of multiset partitions of multisets of size n.
%e A318566 Non-isomorphic representatives of the a(3) = 21 multiset partitions of multiset partitions:
%e A318566   {{{1,1,1}}}
%e A318566   {{{1,1,2}}}
%e A318566   {{{1,2,3}}}
%e A318566   {{{1},{1,1}}}
%e A318566   {{{1},{1,2}}}
%e A318566   {{{1},{2,3}}}
%e A318566   {{{2},{1,1}}}
%e A318566   {{{1},{1},{1}}}
%e A318566   {{{1},{1},{2}}}
%e A318566   {{{1},{2},{3}}}
%e A318566   {{{1}},{{1,1}}}
%e A318566   {{{1}},{{1,2}}}
%e A318566   {{{1}},{{2,3}}}
%e A318566   {{{2}},{{1,1}}}
%e A318566   {{{1}},{{1},{1}}}
%e A318566   {{{1}},{{1},{2}}}
%e A318566   {{{1}},{{2},{3}}}
%e A318566   {{{2}},{{1},{1}}}
%e A318566   {{{1}},{{1}},{{1}}}
%e A318566   {{{1}},{{1}},{{2}}}
%e A318566   {{{1}},{{2}},{{3}}}
%t A318566 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A318566 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A318566 strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
%t A318566 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]]]}]]];
%t A318566 Table[Length[Union[dubnorm/@Join@@mps/@Join@@mps/@strnorm[n]]],{n,5}]
%o A318566 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A318566 seq(n)={my(A=sExp(symGroupSeries(n))); NumUnlabeledObjsSeq(sCartProd(A, sExp(A)-1))} \\ _Andrew Howroyd_, Dec 30 2020
%Y A318566 Cf. A001970, A007716, A050336, A050338, A255906, A269134, A317533, A317791, A318564, A318565.
%K A318566 nonn
%O A318566 1,2
%A A318566 _Gus Wiseman_, Aug 29 2018
%E A318566 Terms a(8) and beyond from _Andrew Howroyd_, Dec 30 2020