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%I #11 Jul 12 2019 20:19:24
%S 1,1,1,2,2,5,5,18,16,75,64,405,302,2581,1693,19872
%N Number of set partitions of {1..n} where every block has the same average.
%H 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 The a(1) = 1 through a(7) = 18 set partitions:
%e {1} {12} {123} {1234} {12345} {123456} {1234567}
%e {13}{2} {14}{23} {1245}{3} {1256}{34} {123567}{4}
%e {135}{24} {1346}{25} {12467}{35}
%e {15}{234} {16}{2345} {1267}{345}
%e {15}{24}{3} {16}{25}{34} {13457}{26}
%e {1357}{246}
%e {1456}{237}
%e {147}{2356}
%e {156}{2347}
%e {17}{23456}
%e {1267}{35}{4}
%e {1357}{26}{4}
%e {147}{26}{35}
%e {156}{237}{4}
%e {17}{2356}{4}
%e {17}{246}{35}
%e {17}{26}{345}
%e {17}{26}{35}{4}
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t Table[Length[Select[sps[Range[n]],SameQ@@Mean/@#&]],{n,0,8}]
%Y Cf. A000110, A007837, A035470, A038041, A275780, A306017, A306021, A319169, A326513, A326515, A326520, A326536.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, Jul 11 2019
%E a(12)-a(15) from _Alois P. Heinz_, Jul 12 2019
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