A362704 - OEIS

%I #11 Apr 30 2023 10:15:44

%S 1,0,1,3,18,130,1140,11886,142408,1934640,29357100,492249340,

%T 9038206056,180352513848,3886286296984,89937276717120,

%U 2224716791224320,58577968147130176,1635780290409117648,48286974141713673072,1502385897082471446880

%N Expansion of e.g.f. 1/(1 + LambertW(-x^2/2 * exp(x))).

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

%F a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-k) / (2^k * k! * (n-2*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2/2*exp(x)))))

%Y Cf. A072034, A362705.

%Y Cf. A362350.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Apr 30 2023