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 A356589 #15 Aug 17 2022 02:42:32
%S A356589 1,7,74,1896,83829,6169915,634444586,89796130088,16407420884385,
%T A356589 3792452363345383,1076168167972120354,368657061467873013440,
%U A356589 149787334364400115372677,71262783791831946810277899,39228224120114488162020163762
%N A356589 a(n) = n! * Sum_{k=1..n} sigma_k(k)/(k * (n-k)!).
%F A356589 E.g.f.: -exp(x) * Sum_{k>0} log(1 - (k*x)^k)/k.
%F A356589 a(n) ~ n! * n^(n-1). - _Vaclav Kotesovec_, Aug 17 2022
%t A356589 a[n_] := n! * Sum[DivisorSigma[k, k]/(k*(n - k)!), {k, 1, n}]; Array[a, 15] (* _Amiram Eldar_, Aug 14 2022 *)
%o A356589 (PARI) a(n) = n!*sum(k=1, n, sigma(k, k)/(k*(n-k)!));
%o A356589 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-(k*x)^k)/k)))
%Y A356589 Cf. A002745, A002746, A356437, A356590.
%K A356589 nonn
%O A356589 1,2
%A A356589 _Seiichi Manyama_, Aug 14 2022