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 A352138 #18 Mar 07 2022 02:09:57
%S A352138 1,0,-2,1,17,-17,-401,817,16197,-49861,-1123633,5354787,105696447,
%T A352138 -682603651,-14697824519,131535803133,2457119246745,-28321054685609,
%U A352138 -572811846560453,8626026427105983,146289547341006011,-2784279036040263575,-51756654994427512331
%N A352138 Expansion of e.g.f. 1/(exp(x) - log(1 + x)).
%F A352138 a(0) = 1; a(n) = -Sum_{k=1..n} ((-1)^k * (k-1)! + 1) * binomial(n,k) * a(n-k).
%t A352138 m = 22; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 + x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 06 2022 *)
%o A352138 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-log(1+x))))
%o A352138 (PARI) a(n) = if(n==0, 1, -sum(k=1, n, ((-1)^k*(k-1)!+1)*binomial(n, k)*a(n-k)));
%Y A352138 Cf. A352139, A352146, A352147.
%Y A352138 Cf. A235378.
%K A352138 sign
%O A352138 0,3
%A A352138 _Seiichi Manyama_, Mar 06 2022