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1, 1, 3, 6, 15, 28, 66, 120, 253, 465, 903, 1596, 3003, 5151, 9180, 15576, 26796, 44253, 74305, 120295, 196878, 314028, 502503, 788140, 1241100, 1917861, 2968266, 4531555, 6913621, 10421895, 15705210, 23409903, 34857075, 51445296, 75774205, 110759286
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of partitions of 2n that are sum-symmetric. That is, a(n) is the number of partitions of 2n that can be divided into two subsequences (no central summand) that each total to n. Example: Of the 11 partitions of 6, there are 6 that are sum-symmetric (partition subsequences bracketed [] and listed in descending order for clarity:) [3][3], [3][2,1], [3][1,1,1], [2,1][2,1], [2,1][1,1,1], [1,1,1][1,1,1]. As this example suggests, a(n) = p(n)*(p(n)+1)/2. - Gregory L. Simay, Oct 26 2015
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LINKS
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MAPLE
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f:= proc(n) local p;
p:= combinat:-numbpart(n);
p*(p+1)/2
end proc:
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MATHEMATICA
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PROG
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(PARI) a(n) = apply(x->x*(x+1)/2, numbpart(n)); \\ Michel Marcus, Oct 26 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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