%I #14 May 01 2023 09:25:11

%S 1,0,3,7,97,811,11941,178557,3354513,69809383,1659853861,43658971753,

%T 1268252733001,40206626846283,1383302292511413,51308059650256741,

%U 2041494097105707937,86734131445797216847,3919172491760452282693,187679722656551406628833

%N Expansion of e.g.f. exp(-LambertW(-x))/(1+x).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: -LambertW(-x)/(x * (1+x)).

%F a(n) = (-1)^n * n! * Sum_{k=0..n} (-(k+1))^k/(k+1)!.

%F a(0) = 1; a(n) = -n*a(n-1) + (n+1)^(n-1).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x))/(1+x)))

%Y Cf. A102743, A277509.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, May 01 2023