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A169888
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Number of n-member subsets of 1..2n whose elements sum to a multiple of n.
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8
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1, 2, 2, 8, 18, 52, 152, 492, 1618, 5408, 18452, 64132, 225432, 800048, 2865228, 10341208, 37568338, 137270956, 504171584, 1860277044, 6892335668, 25631327688, 95640829924, 357975249028, 1343650267288, 5056424257552, 19073789328752, 72108867620204
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OFFSET
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0,2
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COMMENTS
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This is twice A145855 (for n>0), which is the main entry for this problem.
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LINKS
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FORMULA
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MAPLE
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with(combinat): t0:=[]; for n from 1 to 8 do ans:=0; t1:=choose(2*n, n); for i in t1 do s1:=add(i[j], j=1..n); if s1 mod n = 0 then ans:=ans+1; fi; od: t0:=[op(t0), ans]; od:
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MATHEMATICA
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PROG
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(PARI) a(n) = if(n==0, 1, sumdiv(n, d, (-1)^(n+d)*eulerphi(n/d)*binomial(2*d, d)/n)); \\ Altug Alkan, Aug 27 2018, after T. D. Noe at A145855
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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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