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 A302581 #9 Jun 09 2019 03:58:43
%S A302581 0,1,-3,20,-186,2249,-33360,586172,-11901008,274098393,-7060189120,
%T A302581 201092672604,-6275340884736,212915635727313,-7803567334571008,
%U A302581 307245946117223700,-12933084380738398208,579587518114690731601,-27550568677612746940416,1384553892443352890245636
%N A302581 a(n) = n! * [x^n] -exp(-n*x)*log(1 - x).
%H A302581 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A302581 <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>
%F A302581 a(n) = Sum_{k=1..n} (-n)^(n-k)*(k-1)!*binomial(n,k).
%F A302581 E.g.f.: -log(1 - LambertW(x))/(1 + LambertW(x)). - _Vaclav Kotesovec_, Jun 09 2019
%F A302581 a(n) ~ -(-1)^n * log(2) * n^n. - _Vaclav Kotesovec_, Jun 09 2019
%t A302581 Table[n! SeriesCoefficient[-Exp[-n x] Log[1 - x], {x, 0, n}], {n, 0, 19}]
%t A302581 Table[Sum[(-n)^(n - k) (k - 1)! Binomial[n, k], {k, 1, n}], {n, 0, 19}]
%t A302581 nmax = 20; CoefficientList[Series[-Log[1 - LambertW[x]]/(1 + LambertW[x]), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Jun 09 2019 *)
%Y A302581 Cf. A002104, A002741, A104150, A134095, A190314.
%K A302581 sign
%O A302581 0,3
%A A302581 _Ilya Gutkovskiy_, Apr 10 2018