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%I #10 Oct 17 2018 09:00:04
%S 6,3,6,15,48,171,678,2871,12858,60084,290814,1448679,7394106,38527779,
%T 204365880,1101000087,6013054788,33239486925,185736687366,
%U 1047961118940,5964676687668,34219227608607,197737647050742,1150211467134927,6731334034067058,39614408616493581,234342269725331130,1392933275876114127
%N a(n) = (2/n^3) * Sum_{d|n} moebius(n/d)*binomial(3*d,d).
%H G. C. Greubel, <a href="/A268618/b268618.txt">Table of n, a(n) for n = 1..1200</a>
%H R. R. Aidagulov, M. A. Alekseyev. On p-adic approximation of sums of binomial coefficients. Journal of Mathematical Sciences 233:5 (2018), 626-634. doi:<a href="http://doi.org/10.1007/s10958-018-3948-0">10.1007/s10958-018-3948-0</a> arXiv:<a href="http://arxiv.org/abs/1602.02632">1602.02632</a>
%F a(n) = (2/n^3)* Sum_{d|n} A008683(n/d)*A005809(d) = (2/n^2)*A060170(n) = (2/n)*A268617(n).
%t a[n_] := (2/n^3)* DivisorSum[n, MoebiusMu[n/#] Binomial[3 #, #] &]; Array[a, 50] (* _G. C. Greubel_, Dec 15 2017 *)
%o (PARI) { a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d, d))*2/n^3; }
%Y Cf. A268592, A254593
%K nonn
%O 1,1
%A _Max Alekseyev_, Feb 09 2016
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