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%I #7 Jul 12 2019 20:19:35
%S 1,1,2,4,12,40,154,650,3024,15110,81538,468494,2863340
%N Number of set partitions of {1..n} where each block has a different 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(4) = 12 set partitions:
%e {{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}}
%e {{1},{2}} {{1},{2,3}} {{1},{2,3,4}}
%e {{1,2},{3}} {{1,2},{3,4}}
%e {{1},{2},{3}} {{1,2,3},{4}}
%e {{1,2,4},{3}}
%e {{1,3},{2,4}}
%e {{1,3,4},{2}}
%e {{1},{2},{3,4}}
%e {{1},{2,3},{4}}
%e {{1,2},{3},{4}}
%e {{1,4},{2},{3}}
%e {{1},{2},{3},{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]],UnsameQ@@Mean/@#&]],{n,0,8}]
%Y Cf. A000110, A007837, A035470, A038041, A275780, A326512, A326516, A326521, A326537.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jul 11 2019
%E a(12) from _Alois P. Heinz_, Jul 12 2019
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