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 A353992 #27 Aug 06 2022 10:14:11
%S A353992 1,7,41,314,2194,22764,195348,2374224,27940176,384636960,4673720160,
%T A353992 95522440320,1323221996160,23481816503040,489968947641600,
%U A353992 10853692580505600,190580382936115200,5408424680491929600,105077728210820198400,3399507785578641408000
%N A353992 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d + 1) )/k.
%F A353992 a(n) = n! * Sum_{k=1..n} A078308(k)/k.
%F A353992 a(n) = n! * Sum_{k=1..n} Sum_{d|k} (k/d)^d / d.
%F A353992 E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - k * x^k).
%t A353992 a[n_] := n! * Sum[DivisorSum[k, #^(k/# + 1) &]/k, {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Aug 06 2022 *)
%o A353992 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d+1))/k);
%o A353992 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (k/d)^d/d));
%o A353992 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k))/(1-x)))
%Y A353992 Cf. A078308, A353993, A356010, A356298, A356406.
%K A353992 nonn
%O A353992 1,2
%A A353992 _Seiichi Manyama_, Aug 06 2022