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 A291979 #27 Aug 30 2024 21:28:03
%S A291979 1,2,6,27,167,1310,12394,137053,1733325,24670114,390204086,6789564639,
%T A291979 128884276179,2650516064222,58701784670138,1392959655437473,
%U A291979 35257885037803417,948208649740610466,27000743345935785670,811575543670852269347,25677856392014665436799
%N A291979 a(n) = (-1)^n*n!*[x^n] exp(-x)/(1 + log(1+x)).
%C A291979 Row sums of A291978.
%H A291979 Seiichi Manyama, <a href="/A291979/b291979.txt">Table of n, a(n) for n = 0..418</a>
%F A291979 a(n) ~ sqrt(2*Pi) * n^(n+1/2) * exp(1 - exp(-1)) / (exp(1)-1)^(n+1). - _Vaclav Kotesovec_, Sep 18 2017
%F A291979 a(n) = 1 + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k). - _Ilya Gutkovskiy_, Apr 26 2021
%F A291979 a(n) = Sum_{k=0..n} Sum_{j=0..k} binomial(n,k)*j!*A132393(k,j). - _Fabian Pereyra_, Aug 29 2024
%p A291979 a_list := proc(n) exp(-x)/(1 + log(1+x)): series(%, x, n+1):
%p A291979 seq((-1)^k*k!*coeff(%, x, k), k=0..n) end: a_list(20);
%t A291979 nmax = 20; CoefficientList[Series[E^(-x)/(1 + Log[1+x]), {x, 0, nmax}], x] * Range[0, nmax]! * (-1)^Range[0, nmax] (* _Vaclav Kotesovec_, Sep 18 2017 *)
%o A291979 (PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+log(1-x)))) \\ _Seiichi Manyama_, Oct 20 2021
%Y A291979 Cf. A132393, A291978, A343707, A343709, A343710.
%K A291979 nonn
%O A291979 0,2
%A A291979 _Peter Luschny_, Sep 16 2017