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A131868
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a(n) = (2*n^2)^(-1)*Sum_{d|n} (-1)^(n+d)*moebius(n/d)*binomial(2*d,d).
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6
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1, 1, 1, 2, 5, 13, 35, 100, 300, 925, 2915, 9386, 30771, 102347, 344705, 1173960, 4037381, 14004912, 48954659, 172307930, 610269695, 2173656683, 7782070631, 27992709172, 101128485150, 366803656323, 1335349400274, 4877991428982
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OFFSET
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1,4
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COMMENTS
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n*a(n) is the number of n-member subsets of {1,2,3,...,2*n-1} that sum to 1 mod n, cf. A145855. - Vladeta Jovovic, Oct 28 2008
a(n) is the number of orbits under the S_n action on a set closely related to the set of parking functions. See Konvalinka-Tewari reference below. - Vasu Tewari, Mar 17 2020
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LINKS
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FORMULA
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MAPLE
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A131868 := proc(n) local a, d ; a := 0 ; for d in numtheory[divisors](n) do a := a+(-1)^(n+d)*numtheory[mobius](n/d)*binomial(2*d, d) ; od: a/2/n^2 ; end: seq(A131868(n), n=1..30) ; # R. J. Mathar, Oct 24 2007
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MATHEMATICA
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a = {}; For[n = 1, n < 30, n++, b = Divisors[n]; s = 0; For[j = 1, j < Length[b] + 1, j++, s = s + (-1)^(n + b[[j]])*MoebiusMu[n/b[[j]]]* Binomial[2*b[[j]], b[[j]]]]; AppendTo[a, s/(2*n^2)]]; a (* Stefan Steinerberger, Oct 26 2007 *)
a[n_] := 1/(2n^2) DivisorSum[n, (-1)^(n+#) MoebiusMu[n/#] Binomial[2#, #]& ]; Array[a, 30] (* Jean-François Alcover, Dec 18 2015 *)
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PROG
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(PARI) a(n) = (2*n^2)^(-1)*sumdiv(n, d, (-1)^(n+d)*moebius(n/d)*binomial(2*d, d)); \\ Michel Marcus, Dec 06 2018
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CROSSREFS
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KEYWORD
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easy,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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