cp's OEIS Frontend

A326519 Number of normal multiset partitions of weight n where each part has a different sum.

%I A326519 #9 Apr 04 2025 01:19:41
%S A326519 1,1,3,11,51,259,1461,9133,62348,459547,3632419
%N A326519 Number of normal multiset partitions of weight n where each part has a different sum.
%C A326519 A multiset partition is normal if it covers an initial interval of positive integers.
%H A326519 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e A326519 The a(0) = 1 through a(3) = 11 normal multiset partitions:
%e A326519   {}  {{1}}  {{1,1}}    {{1,1,1}}
%e A326519              {{1,2}}    {{1,1,2}}
%e A326519              {{1},{2}}  {{1,2,2}}
%e A326519                         {{1,2,3}}
%e A326519                         {{1},{1,1}}
%e A326519                         {{1},{1,2}}
%e A326519                         {{1},{2,2}}
%e A326519                         {{1},{2,3}}
%e A326519                         {{2},{1,2}}
%e A326519                         {{2},{1,3}}
%e A326519                         {{1},{2},{3}}
%t A326519 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A326519 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A326519 allnorm[n_]:=If[n<=0,{{}},Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]];
%t A326519 Table[Length[Select[Join@@mps/@allnorm[n],UnsameQ@@Total/@#&]],{n,0,5}]
%Y A326519 Cf. A038041, A255906, A275780, A317583, A321469, A326517, A326518, A326520, A326521, A326535.
%K A326519 nonn,more
%O A326519 0,3
%A A326519 _Gus Wiseman_, Jul 12 2019
%E A326519 a(8)-a(10) from _Robert Price_, Apr 03 2025