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 A330493 #18 Dec 16 2019 11:40:57
%S A330493 1,3,12,70,492,4298,43894,514666,6830888,101473632,1664125944,
%T A330493 29858266392,582481147440,12281821373040,278257595964576,
%U A330493 6739505703156192,173785740554811264,4754455742416944000,137571331202872821504,4197696814883284962048
%N A330493 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * tau(k), where tau = A000005.
%H A330493 Vaclav Kotesovec, <a href="/A330493/b330493.txt">Table of n, a(n) for n = 1..400</a>
%F A330493 E.g.f.: -Sum_{k>=1} log(1 - log(1/(1 - x))^k) / k.
%F A330493 a(n) ~ n! * (log(n) + 2*gamma - log(exp(1) - 1)) / (n * (1 - exp(-1))^n), where gamma is the Euler-Mascheroni constant A001620.
%t A330493 Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}]
%t A330493 nmax = 20; Rest[CoefficientList[Series[-Sum[Log[1 - Log[1/(1 - x)]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!]
%o A330493 (PARI) a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1)*(k-1)!*numdiv(k)); \\ _Michel Marcus_, Dec 16 2019
%Y A330493 Cf. A330351, A330352, A330494, A330495.
%K A330493 nonn
%O A330493 1,2
%A A330493 _Vaclav Kotesovec_, Dec 16 2019