This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326518 #10 Apr 04 2025 10:20:12
%S A326518 1,1,3,7,15,31,75,169,445,1199,3471
%N A326518 Number of normal multiset partitions of weight n where every part has the same sum.
%C A326518 A multiset partition is normal if it covers an initial interval of positive integers.
%H A326518 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 A326518 The a(0) = 1 through a(4) = 15 normal multiset partitions:
%e A326518 {} {{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}}
%e A326518 {{1,2}} {{1,1,2}} {{1,1,1,2}}
%e A326518 {{1},{1}} {{1,2,2}} {{1,1,2,2}}
%e A326518 {{1,2,3}} {{1,1,2,3}}
%e A326518 {{2},{1,1}} {{1,2,2,2}}
%e A326518 {{3},{1,2}} {{1,2,2,3}}
%e A326518 {{1},{1},{1}} {{1,2,3,3}}
%e A326518 {{1,2,3,4}}
%e A326518 {{1,1},{1,1}}
%e A326518 {{1,2},{1,2}}
%e A326518 {{1,3},{2,2}}
%e A326518 {{1,4},{2,3}}
%e A326518 {{2},{2},{1,1}}
%e A326518 {{3},{3},{1,2}}
%e A326518 {{1},{1},{1},{1}}
%t A326518 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A326518 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A326518 allnorm[n_]:=If[n<=0,{{}},Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]];
%t A326518 Table[Length[Select[Join@@mps/@allnorm[n],SameQ@@Total/@#&]],{n,0,5}]
%Y A326518 Cf. A035470, A038041, A255906, A317583, A321455, A326517, A326519, A326520, A326521, A326534.
%K A326518 nonn
%O A326518 0,3
%A A326518 _Gus Wiseman_, Jul 12 2019
%E A326518 a(10) from _Robert Price_, Apr 04 2025