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 A356323 #15 Aug 07 2022 04:44:41
%S A356323 1,11,89,794,6994,72204,753108,8973264,111281616,1524322080,
%T A356323 21601104480,340803192960,5483287025280,96044874750720,
%U A356323 1748238132614400,34093033838438400,682396164763084800,14706429413353574400,323342442475011993600,7585740483060676608000
%N A356323 a(n) = n! * Sum_{k=1..n} sigma_3(k)/k.
%F A356323 E.g.f.: (1/(1-x)) * Sum_{k>0} x^k * (1 + x^k)/(k * (1 - x^k)^3).
%F A356323 E.g.f.: -(1/(1-x)) * Sum_{k>0} k^2 * log(1 - x^k).
%F A356323 a(n) ~ n! * Pi^4 * n^3 / 270. - _Vaclav Kotesovec_, Aug 07 2022
%t A356323 Table[n! * Sum[DivisorSigma[3, k]/k, {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o A356323 (PARI) a(n) = n!*sum(k=1, n, sigma(k, 3)/k);
%o A356323 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*(1+x^k)/(k*(1-x^k)^3))/(1-x)))
%o A356323 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k^2*log(1-x^k))/(1-x)))
%Y A356323 Cf. A001158, A064603, A356010, A356297, A356298.
%K A356323 nonn
%O A356323 1,2
%A A356323 _Seiichi Manyama_, Aug 03 2022