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 A356390 #18 Aug 18 2022 05:58:52
%S A356390 1,3,17,74,514,3564,30708,250704,2780496,29982240,373350240,
%T A356390 4639870080,67024333440,988156834560,16914631507200,271941778483200,
%U A356390 4999620452198400,94617104704819200,1925772463506124800,39245319872575488000,902004581585737728000
%N A356390 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d + 1) * d ) /k.
%H A356390 Seiichi Manyama, <a href="/A356390/b356390.txt">Table of n, a(n) for n = 1..448</a>
%F A356390 a(n) = n! * Sum_{k=1..n} A000593(k)/k.
%F A356390 E.g.f.: -(1/(1-x)) * Sum_{k>0} (-x)^k/(k * (1 - x^k)).
%F A356390 E.g.f.: (1/(1-x)) * Sum_{k>0} log(1 + x^k).
%F A356390 a(n) ~ n! * n * Pi^2/12. - _Vaclav Kotesovec_, Aug 07 2022
%t A356390 Table[n! * Sum[Sum[(-1)^(k/d + 1)*d, {d, Divisors[k]}]/k, {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o A356390 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d)/k);
%o A356390 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (-x)^k/(k*(1-x^k)))/(1-x)))
%o A356390 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k))/(1-x)))
%Y A356390 Cf. A356389, A356391.
%Y A356390 Cf. A000593, A356010, A356393.
%K A356390 nonn
%O A356390 1,2
%A A356390 _Seiichi Manyama_, Aug 05 2022