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A268592 a(n) = (6/n^3) * Sum_{d|n} moebius(n/d)*binomial(2*d,d). 8
12, 3, 4, 6, 12, 25, 60, 150, 400, 1107, 3180, 9386, 28404, 87711, 275764, 880470, 2849916, 9336508, 30918732, 103384758, 348725540, 1185630123, 4060210764, 13996354586, 48541672872, 169293988125, 593488622344, 2090567755278, 7396924802052, 26281018091013, 93738717046476, 335563502259798 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1500

R. R. Aidagulov and M. A. Alekseyev. On p-adic approximation of sums of binomial coefficients. Journal of Mathematical Sciences, 2016. (in press)

FORMULA

a(n) = A007727(n)*6/n^3 = A045630(n)*12/n^3 = A060165(n)*6/n^2 = A022553(n)*12/n^2 = A268619(n)*6/n.

For n == 0, 1, or 3 (mod 4), a(n) = 2*A254593(n); for n == 2 (mod 4), a(n) = 2*A254593(n) - A254593(n/2)/2.

MATHEMATICA

a[n_] := (6/n^3)* DivisorSum[n, MoebiusMu[n/#] Binomial[2 #, #] &]; Array[a, 50] (* G. C. Greubel, Dec 15 2017 *)

PROG

(PARI) { a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d))*6/n^3; }

CROSSREFS

Cf. A254593, A268618, A268619.

Sequence in context: A129197 A098067 A070604 * A127146 A063609 A040139

Adjacent sequences:  A268589 A268590 A268591 * A268593 A268594 A268595

KEYWORD

nonn

AUTHOR

Max Alekseyev, Feb 07 2016

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)