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%I #16 Apr 17 2023 17:24:03
%S 1,1,3,7,61,261,3991,24403,524217,4149001,114544171,1111976031,
%T 37492210933,431097055117,17165526306111,228085258466731,
%U 10472666396599921,157882659583461393,8211536252680154707,138474928851961700791,8045878340298511456941
%N a(n) = n! * Sum_{k=0..floor(n/2)} k^k / (k! * (n-2*k)!).
%H Winston de Greef, <a href="/A362347/b362347.txt">Table of n, a(n) for n = 0..414</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)).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2))))
%Y Cf. A086331, A362348, A362349.
%Y Cf. A277614.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 17 2023