A346577 a(n) = (1/(3*n)) * Sum_{d|n} mu(n/d) * binomial(3*d,d).

1, 2, 9, 40, 200, 1026, 5537, 30624, 173583, 1001400, 5864749, 34768296, 208267319, 1258574114, 7663720500, 46976003712, 289628805622, 1794932293950, 11175157356521, 69864074596000, 438403736543598, 2760351027094298, 17433869214973753, 110420300844952992

Offset: 1

Author

Ilya Gutkovskiy, Jul 24 2021

Keywords

• nonn

Comments

Inverse Euler transform of A001764.

Moebius transform of A082936.

Crossrefs

Cf. A001764, A005809, A008683, A022553, A060170, A082936, A346578, A346579, A346580, A346581, A346582.

Programs

Mathematica

Table[(1/(3 n)) Sum[MoebiusMu[n/d] Binomial[3 d, d], {d, Divisors[n]}], {n, 24}]

PARI

a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d,d))/(3*n); \\ Michel Marcus, Jul 24 2021

Formula

a(n) = A060170(n)/3. - Hugo Pfoertner, Jul 24 2021