cp's OEIS Frontend

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

%I A318565 #10 Dec 30 2020 17:12:00
%S A318565 1,6,27,169,1029,7817,61006,547537,5202009,54506262,606311524,
%T A318565 7299051826,92985064466,1264720212352,18137495642192,275078184766323,
%U A318565 4379514178076452,73235806332442156,1280229713195027792,23381809052104639236,444740694108284116235,8801030741502964613534
%N A318565 Number of multiset partitions of multiset partitions of strongly normal multisets of size n.
%C A318565 A multiset is normal if it spans an initial interval of positive integers, and strongly normal if in addition it has weakly decreasing multiplicities.
%e A318565 The a(2) = 6 multiset partitions of multiset partitions:
%e A318565   {{{1,1}}}
%e A318565   {{{1,2}}}
%e A318565   {{{1},{1}}}
%e A318565   {{{1},{2}}}
%e A318565   {{{1}},{{1}}}
%e A318565   {{{1}},{{2}}}
%t A318565 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A318565 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A318565 strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
%t A318565 Table[Sum[Length[mps[m]],{m,Join@@mps/@strnorm[n]}],{n,6}]
%o A318565 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A318565 seq(n)={my(A=symGroupSeries(n)); StronglyNormalLabelingsSeq(sExp(sExp(A))-1)} \\ _Andrew Howroyd_, Dec 30 2020
%Y A318565 Cf. A001970, A007716, A050336, A255906, A269134, A317533, A317791, A318564, A318566.
%K A318565 nonn
%O A318565 1,2
%A A318565 _Gus Wiseman_, Aug 29 2018
%E A318565 Terms a(9) and beyond from _Andrew Howroyd_, Dec 30 2020