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A332467 a(n) = n! * Sum_{d|n} mu(d) / (d!)^(n/d). 1

%I

%S 1,1,5,18,119,611,5039,37800,361200,3515149,39916799,471148524,

%T 6227020799,86497207369,1307505443245,20841060240000,355687428095999,

%U 6389731861649136,121645100408831999,2430526115576719732,51090759661943327041,1123451899297246814569

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

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

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

%F a(n) ~ n!. - _Vaclav Kotesovec_, Feb 16 2020

%t Table[n! DivisorSum[n, MoebiusMu[#]/(#!)^(n/#) &], {n, 1, 22}]

%t nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] x^k/(k! - x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%o (PARI) a(n)={sumdiv(n, d, moebius(d)*n!/(d!)^(n/d))} \\ _Andrew Howroyd_, Feb 13 2020

%o (MAGMA) [Factorial(n)*&+[MoebiusMu(d) /(Factorial(d))^(n div d):d in Divisors(n)]:n in [1..22]]; // _Marius A. Burtea_, Feb 13 2020

%Y Cf. A008683, A061095, A327587, A332466.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Feb 13 2020

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)