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A362046
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Number of nonempty subsets of {1..n} with mean n/2.
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9
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0, 0, 1, 1, 3, 3, 9, 8, 25, 23, 75, 68, 235, 213, 759, 695, 2521, 2325, 8555, 7941, 29503, 27561, 103129, 96861, 364547, 344003, 1300819, 1232566, 4679471, 4449849, 16952161, 16171117, 61790441, 59107889, 226451035, 217157068, 833918839, 801467551, 3084255127
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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The a(2) = 1 through a(7) = 8 subsets:
{1} {1,2} {2} {1,4} {3} {1,6}
{1,3} {2,3} {1,5} {2,5}
{1,2,3} {1,2,3,4} {2,4} {3,4}
{1,2,6} {1,2,4,7}
{1,3,5} {1,2,5,6}
{2,3,4} {1,3,4,6}
{1,2,3,6} {2,3,4,5}
{1,2,4,5} {1,2,3,4,5,6}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Mean[#]==n/2&]], {n, 0, 15}]
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CROSSREFS
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Including the empty set gives A133406.
A000980 counts nonempty subsets of {1..2n-1} with mean n.
A327481 counts subsets by integer mean.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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