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A131868 a(n) = (2*n^2)^(-1)*Sum_{d|n} (-1)^(n+d)*moebius(n/d)*binomial(2*d,d). 7
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; text; internal format)
OFFSET

1,4

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. - Vladeta Jovovic, Oct 28 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

J. Malenfant, On the Matrix-Element Expansion of a Circulant Determinant, arXiv:1502.06012 [math.NT], 2015.

Steven Rayan, Aspects of the topology and combinatorics of Higgs bundle moduli spaces, arXiv:1809.05732 [math.AG], 2018.

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, Oct 24 2007

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, 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 *)

PROG

(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

CROSSREFS

Cf. A022553.

Sequence in context: A234643 A089846 A258450 * A272064 A000747 A151259

Adjacent sequences:  A131865 A131866 A131867 * A131869 A131870 A131871

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Oct 04 2007

EXTENSIONS

More terms from R. J. Mathar and Stefan Steinerberger, Oct 24 2007

STATUS

approved

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Last modified May 22 05:45 EDT 2019. Contains 323473 sequences. (Running on oeis4.)