%I #14 Aug 24 2023 02:31:06
%S 3,3,9,30,120,513,2373,11484,57861,300420,1599477,8692074,48061689,
%T 269694453,1532744100,8808000696,51110965698,299155382325,
%U 1764498529977,10479611189400,62629105220514,376411503694677,2273982941083533,13802537605619124,84141675425838225,514987312014416553,3163620641291970255
%N a(n) = (1/n^2) * Sum_{d|n} moebius(n/d)*binomial(3*d,d).
%C 2*a(n) is divisible by n (cf. A268618).
%F a(n) = (1/n^2)* Sum_{d|n} A008683(n/d)*A005809(d).
%F a(n) = A060170(n) / n = A268618(n)*n/2.
%t a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[3*#, #] &] / n^2; Array[a, 30] (* _Amiram Eldar_, Aug 24 2023 *)
%o (PARI) { a(n) = sumdiv(n,d,moebius(n/d)*binomial(3*d,d))/n^2; }
%Y Cf. A005809, A008683, A060170, A268618, A268619.
%K nonn
%O 1,1
%A _Max Alekseyev_, Feb 09 2016
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