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%I #11 Apr 29 2023 08:38:34
%S 1,1,-1,10,-51,556,-7085,116376,-2263303,51072400,-1308626649,
%T 37526799520,-1190440709051,41385630158016,-1564585725985477,
%U 63903022429837696,-2804097015221308815,131558782973452677376,-6571623885587502740657
%N E.g.f. satisfies A(x) = exp( x * exp(x^2) / A(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.: exp( LambertW(x * exp(x^2)) ).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (-n+2*k+1)^(n-2*k-1) / (k! * (n-2*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*exp(x^2)))))
%Y Cf. A362674.
%K sign
%O 0,4
%A _Seiichi Manyama_, Apr 29 2023