A268618 a(n) = (2/n^3) * Sum_{d|n} moebius(n/d)*binomial(3*d,d).

6, 3, 6, 15, 48, 171, 678, 2871, 12858, 60084, 290814, 1448679, 7394106, 38527779, 204365880, 1101000087, 6013054788, 33239486925, 185736687366, 1047961118940, 5964676687668, 34219227608607, 197737647050742, 1150211467134927, 6731334034067058, 39614408616493581, 234342269725331130, 1392933275876114127

Offset: 1

Author

Max Alekseyev, Feb 09 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1200
• 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:10.1007/s10958-018-3948-0 arXiv:1602.02632

Crossrefs

Cf. A268592, A254593

Programs

Mathematica

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

PARI

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

Formula

a(n) = (2/n^3)* Sum_{d|n} A008683(n/d)*A005809(d) = (2/n^2)*A060170(n) = (2/n)*A268617(n).