A268617 a(n) = (1/n^2) * Sum_{d|n} moebius(n/d)*binomial(3*d,d).

3, 3, 9, 30, 120, 513, 2373, 11484, 57861, 300420, 1599477, 8692074, 48061689, 269694453, 1532744100, 8808000696, 51110965698, 299155382325, 1764498529977, 10479611189400, 62629105220514, 376411503694677, 2273982941083533, 13802537605619124, 84141675425838225, 514987312014416553, 3163620641291970255

Offset: 1

Author

Max Alekseyev, Feb 09 2016

Keywords

• nonn

Comments

2*a(n) is divisible by n (cf. A268618).

Crossrefs

Cf. A005809, A008683, A060170, A268618, A268619.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[3*#, #] &] / n^2; Array[a, 30] (* Amiram Eldar, Aug 24 2023 *)

PARI

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

Formula

a(n) = (1/n^2)* Sum_{d|n} A008683(n/d)*A005809(d).

a(n) = A060170(n) / n = A268618(n)*n/2.