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%I #16 Apr 18 2023 09:42:39
%S 1,1,2,4,19,71,601,3277,39089,277489,4250341,37110701,693581197,
%T 7184750509,158461520309,1899055549861,48269252293201,656869268651537,
%U 18903165795857089,287927838327392929,9252988524143245181,155954097639111859501
%N a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)^k / (k! * (n-2*k)!).
%H Winston de Greef, <a href="/A362350/b362350.txt">Table of n, a(n) for n = 0..437</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp(x) / (1 + LambertW(-x^2/2)).
%F a(n) ~ (exp(2^(3/2)*exp(-1/2)) + (-1)^n) * n^n / (2^((n+1)/2) * exp(n/2 + sqrt(2)*exp(-1/2))). - _Vaclav Kotesovec_, Apr 18 2023
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2/2))))
%Y Cf. A362351, A362352.
%Y Cf. A277614.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 17 2023
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