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 A354851 #13 Jun 08 2022 14:23:39
%S A354851 1,3,8,54,144,2880,5760,206640,1491840,24675840,43545600,10298534400,
%T A354851 6706022400,1195587993600,33476463820800,775450900224000,
%U A354851 376610217984000,553805325545472000,128047474114560000,339876410542276608000,6208765924866785280000
%N A354851 a(n) = (n-1)! * Sum_{d|n} d^(n/d).
%F A354851 a(n) = (n-1)! * A055225(n).
%F A354851 E.g.f.: -Sum_{k>0} log(1 - k * x^k)/k.
%F A354851 If p is prime, a(p) = (p-1)! + p!.
%t A354851 a[n_] := (n - 1)! * DivisorSum[n, #^(n/#) &]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2022 *)
%o A354851 (PARI) a(n) = (n-1)!*sumdiv(n, d, d^(n/d));
%o A354851 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))
%Y A354851 Cf. A055225, A318249, A354848.
%K A354851 nonn
%O A354851 1,2
%A A354851 _Seiichi Manyama_, Jun 08 2022