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A327481
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Triangle read by rows where T(n,k) is the number of nonempty subsets of {1..n} with mean k.
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29
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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, 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, 93, 31, 9, 3, 1, 1, 3, 9, 31, 105, 235, 235, 105, 31, 9, 3, 1
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OFFSET
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1,5
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COMMENTS
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All terms are odd.
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LINKS
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EXAMPLE
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Triangle begins:
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 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 93 31 9 3 1
1 3 9 31 105 235 235 105 31 9 3 1
The subsets counted in row n = 5:
{1} {2} {3} {4} {5}
{1,3} {1,5} {3,5}
{1,2,3} {2,4} {3,4,5}
{1,3,5}
{2,3,4}
{1,2,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Mean[#]==k&]], {n, 10}, {k, n}]
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CROSSREFS
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The sequence of rows converges to A066571.
The version for partitions is A327482.
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KEYWORD
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AUTHOR
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STATUS
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approved
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