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%I #9 Feb 13 2020 15:06:23
%S 1,1,5,12,119,241,5039,20160,302400,1784161,39916799,160332480,
%T 6227020799,43571848321,1078831353601,10461394944000,355687428095999,
%U 2143016754278400,121645100408831999,1196177491129420800,42565648051390464001,562000335730215782401
%N a(n) = n! * Sum_{d|n} mu(d) / d!.
%F E.g.f.: Sum_{k>=1} Sum_{j>=1} mu(j) * x^(k*j) / j!).
%F E.g.f.: Sum_{k>=1} mu(k) * x^k / (k!*(1 - x^k)).
%p with(numtheory):
%p a:= n-> n! * add(mobius(d)/d!, d=divisors(n)):
%p seq(a(n), n=1..23); # _Alois P. Heinz_, Feb 13 2020
%t Table[n! DivisorSum[n, MoebiusMu[#]/#! &], {n, 1, 22}]
%t nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] x^k/(k! (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%o (PARI) a(n)={sumdiv(n, d, moebius(d)*n!/d!)} \\ _Andrew Howroyd_, Feb 13 2020
%Y Cf. A008683, A057625, A068107, A099740, A132958, A332467.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Feb 13 2020
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