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 A332467 #15 Dec 20 2024 03:55:56
%S A332467 1,1,5,18,119,611,5039,37800,361200,3515149,39916799,471148524,
%T A332467 6227020799,86497207369,1307505443245,20841060240000,355687428095999,
%U A332467 6389731861649136,121645100408831999,2430526115576719732,51090759661943327041,1123451899297246814569
%N A332467 a(n) = n! * Sum_{d|n} mu(d) / (d!)^(n/d).
%F A332467 E.g.f.: Sum_{k>=1} Sum_{j>=1} mu(j) * x^(k*j) / (j!)^k.
%F A332467 E.g.f.: Sum_{k>=1} mu(k) * x^k / (k! - x^k).
%F A332467 a(n) ~ n!. - _Vaclav Kotesovec_, Feb 16 2020
%t A332467 Table[n! DivisorSum[n, MoebiusMu[#]/(#!)^(n/#) &], {n, 1, 22}]
%t A332467 nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] x^k/(k! - x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%o A332467 (PARI) a(n)={sumdiv(n, d, moebius(d)*n!/(d!)^(n/d))} \\ _Andrew Howroyd_, Feb 13 2020
%o A332467 (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 A332467 Cf. A008683, A061095, A327587, A332466.
%K A332467 nonn
%O A332467 1,3
%A A332467 _Ilya Gutkovskiy_, Feb 13 2020