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 A362682 #17 Aug 05 2025 06:30:04
%S A362682 1,0,3,7,97,811,11941,178557,3354513,69809383,1659853861,43658971753,
%T A362682 1268252733001,40206626846283,1383302292511413,51308059650256741,
%U A362682 2041494097105707937,86734131445797216847,3919172491760452282693,187679722656551406628833
%N A362682 Expansion of e.g.f. exp(-LambertW(-x))/(1+x).
%H A362682 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362682 E.g.f.: -LambertW(-x)/(x * (1+x)).
%F A362682 a(n) = (-1)^n * n! * Sum_{k=0..n} (-(k+1))^k/(k+1)!.
%F A362682 a(0) = 1; a(n) = -n*a(n-1) + (n+1)^(n-1).
%F A362682 a(n) ~ exp(2) * n^(n-1) / (1 + exp(1)). - _Vaclav Kotesovec_, Aug 05 2025
%o A362682 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x))/(1+x)))
%Y A362682 Cf. A102743, A277509.
%K A362682 nonn,easy
%O A362682 0,3
%A A362682 _Seiichi Manyama_, May 01 2023