A332467 a(n) = n! * Sum_{d|n} mu(d) / (d!)^(n/d).

1, 1, 5, 18, 119, 611, 5039, 37800, 361200, 3515149, 39916799, 471148524, 6227020799, 86497207369, 1307505443245, 20841060240000, 355687428095999, 6389731861649136, 121645100408831999, 2430526115576719732, 51090759661943327041, 1123451899297246814569

Offset: 1

Author

Ilya Gutkovskiy, Feb 13 2020

Keywords

• nonn

Crossrefs

Cf. A008683, A061095, A327587, A332466.

Programs

Magma

[Factorial(n)*&+[MoebiusMu(d) /(Factorial(d))^(n div d):d in Divisors(n)]:n in [1..22]]; // Marius A. Burtea, Feb 13 2020

Mathematica

Table[n! DivisorSum[n, MoebiusMu[#]/(#!)^(n/#) &], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] x^k/(k! - x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

PARI

a(n)={sumdiv(n, d, moebius(d)*n!/(d!)^(n/d))} \\ Andrew Howroyd, Feb 13 2020

Formula

E.g.f.: Sum_{k>=1} Sum_{j>=1} mu(j) * x^(k*j) / (j!)^k.

E.g.f.: Sum_{k>=1} mu(k) * x^k / (k! - x^k).

a(n) ~ n!. - Vaclav Kotesovec, Feb 16 2020