This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332466 #13 Dec 20 2024 03:55:46
%S A332466 1,1,5,12,119,241,5039,20160,302400,1784161,39916799,160332480,
%T A332466 6227020799,43571848321,1078831353601,10461394944000,355687428095999,
%U A332466 2143016754278400,121645100408831999,1196177491129420800,42565648051390464001,562000335730215782401
%N A332466 a(n) = n! * Sum_{d|n} mu(d) / d!.
%F A332466 E.g.f.: Sum_{k>=1} Sum_{j>=1} mu(j) * x^(k*j) / j!.
%F A332466 E.g.f.: Sum_{k>=1} mu(k) * x^k / (k!*(1 - x^k)).
%p A332466 with(numtheory):
%p A332466 a:= n-> n! * add(mobius(d)/d!, d=divisors(n)):
%p A332466 seq(a(n), n=1..23); # _Alois P. Heinz_, Feb 13 2020
%t A332466 Table[n! DivisorSum[n, MoebiusMu[#]/#! &], {n, 1, 22}]
%t A332466 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 A332466 (PARI) a(n)={sumdiv(n, d, moebius(d)*n!/d!)} \\ _Andrew Howroyd_, Feb 13 2020
%Y A332466 Cf. A008683, A057625, A068107, A099740, A132958, A332467.
%K A332466 nonn
%O A332466 1,3
%A A332466 _Ilya Gutkovskiy_, Feb 13 2020