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%I #7 Sep 13 2019 17:05:11
%S 1,1,1,1,3,1,1,3,3,1,1,3,7,3,1,1,3,9,9,3,1,1,3,9,19,9,3,1,1,3,9,25,25,
%T 9,3,1,1,3,9,29,51,29,9,3,1,1,3,9,31,75,75,31,9,3,1,1,3,9,31,93,151,
%U 93,31,9,3,1,1,3,9,31,105,235,235,105,31,9,3,1
%N Triangle read by rows where T(n,k) is the number of nonempty subsets of {1..n} with mean k.
%C All terms are odd.
%e Triangle begins:
%e 1
%e 1 1
%e 1 3 1
%e 1 3 3 1
%e 1 3 7 3 1
%e 1 3 9 9 3 1
%e 1 3 9 19 9 3 1
%e 1 3 9 25 25 9 3 1
%e 1 3 9 29 51 29 9 3 1
%e 1 3 9 31 75 75 31 9 3 1
%e 1 3 9 31 93 151 93 31 9 3 1
%e 1 3 9 31 105 235 235 105 31 9 3 1
%e The subsets counted in row n = 5:
%e {1} {2} {3} {4} {5}
%e {1,3} {1,5} {3,5}
%e {1,2,3} {2,4} {3,4,5}
%e {1,3,5}
%e {2,3,4}
%e {1,2,4,5}
%e {1,2,3,4,5}
%t Table[Length[Select[Subsets[Range[n]],Mean[#]==k&]],{n,10},{k,n}]
%Y Row sums are A051293.
%Y The sequence of rows converges to A066571.
%Y The version for partitions is A327482.
%Y Cf. A000016, A063776, A065795, A135342, A327474, A327475, A327483, A327484.
%K nonn,tabl
%O 1,5
%A _Gus Wiseman_, Sep 13 2019
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