A268619 a(n) = (1/n^2) * Sum_{d|n} moebius(n/d)*binomial(2*d,d).

2, 1, 2, 4, 10, 25, 70, 200, 600, 1845, 5830, 18772, 61542, 204659, 689410, 2347920, 8074762, 28009524, 97909318, 344615860, 1220539390, 4347310451, 15564141262, 55985418344, 202256970300, 733607281875, 2670698800548, 9755982857964, 35751803209918, 131405090455065, 484316704740126, 1789672012052256

Offset: 1

Author

Max Alekseyev, Feb 09 2016

Keywords

• nonn

Comments

6*a(n) is divisible by n (cf. A268592).

Crossrefs

Cf. A000984, A007727, A008683, A022553, A045630, A060165, A268592, A268617.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[2*#, #] &] / n^2; Array[a, 35] (* Amiram Eldar, Aug 24 2023 *)

PARI

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

Formula

a(n) = (1/n^2)* Sum_{d|n} A008683(n/d)*A000984(d).

a(n) = A007727(n)/n^2 = A045630(n)*2/n^2 = A060165(n)/n = A022553(n)*2/n.