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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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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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. [From Vladeta Jovovic (vladeta(AT)eunet.yu), Oct 28 2008]
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MAPLE
| 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 (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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MATHEMATICA
| 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 (stefan.steinerberger(AT)gmail.com), Oct 26 2007
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CROSSREFS
| Cf. A022553.
Sequence in context: A126221 A107086 A089846 * A000747 A151259 A149853
Adjacent sequences: A131865 A131866 A131867 * A131869 A131870 A131871
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 24 2007
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