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 A362693 #26 Feb 16 2025 08:34:05
%S A362693 1,2,0,8,-64,832,-13568,269824,-6328320,171044864,-5235245056,
%T A362693 178988498944,-6760886435840,279614956503040,-12566949343002624,
%U A362693 609881495812702208,-31785828867471572992,1770660964785178279936,-104990165030126886060032
%N A362693 E.g.f. satisfies A(x) = exp(x + x / A(x)).
%H A362693 Seiichi Manyama, <a href="/A362693/b362693.txt">Table of n, a(n) for n = 0..372</a>
%H A362693 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362693 E.g.f.: x / LambertW(x*exp(-x)) = exp( x + LambertW(x*exp(-x)) ).
%F A362693 a(n) = Sum_{k=0..n} (-k+1)^(n-1) * binomial(n,k) = 2^n * A349719(n).
%t A362693 nmax = 20; A[_] = 1;
%t A362693 Do[A[x_] = Exp[x + x/A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
%t A362693 CoefficientList[A[x], x]*Range[0, nmax]! (* _Jean-François Alcover_, Mar 04 2024 *)
%o A362693 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x*exp(-x)))))
%Y A362693 Cf. A349562, A362694, A362734, A362735.
%Y A362693 Cf. A362736, A362737.
%Y A362693 Cf. A349719.
%K A362693 sign
%O A362693 0,2
%A A362693 _Seiichi Manyama_, May 01 2023