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 A326512 #15 Aug 22 2024 20:22:57
%S A326512 1,1,1,2,2,5,5,18,16,75,64,405,302,2581,1693,19872,11295,175807,87524,
%T A326512 1851135,787515,21909766,8185713,298698113,96514608,4538610230,
%U A326512 1285072142
%N A326512 Number of set partitions of {1..n} where every block has the same average.
%C A326512 The common average is necessarily (n+1)/2. The number of blocks with this average is given by A070925. - _Christian Sievers_, Aug 22 2024
%H A326512 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 A326512 The a(1) = 1 through a(7) = 18 set partitions:
%e A326512 {1} {12} {123} {1234} {12345} {123456} {1234567}
%e A326512 {13}{2} {14}{23} {1245}{3} {1256}{34} {123567}{4}
%e A326512 {135}{24} {1346}{25} {12467}{35}
%e A326512 {15}{234} {16}{2345} {1267}{345}
%e A326512 {15}{24}{3} {16}{25}{34} {13457}{26}
%e A326512 {1357}{246}
%e A326512 {1456}{237}
%e A326512 {147}{2356}
%e A326512 {156}{2347}
%e A326512 {17}{23456}
%e A326512 {1267}{35}{4}
%e A326512 {1357}{26}{4}
%e A326512 {147}{26}{35}
%e A326512 {156}{237}{4}
%e A326512 {17}{2356}{4}
%e A326512 {17}{246}{35}
%e A326512 {17}{26}{345}
%e A326512 {17}{26}{35}{4}
%t A326512 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A326512 Table[Length[Select[sps[Range[n]],SameQ@@Mean/@#&]],{n,0,8}]
%Y A326512 Cf. A000110, A007837, A035470, A038041, A070925, A275780, A306017, A306021, A319169, A326513, A326515, A326520, A326536.
%K A326512 nonn,more
%O A326512 0,4
%A A326512 _Gus Wiseman_, Jul 11 2019
%E A326512 a(12)-a(15) from _Alois P. Heinz_, Jul 12 2019
%E A326512 a(16)-a(26) from _Christian Sievers_, Aug 22 2024