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%I #17 Aug 19 2023 22:45:22
%S 1,1,0,1,-6,46,-440,5076,-68740,1070056,-18835164,369994780,
%T -8025080096,190501729848,-4912802070280,136775150153656,
%U -4088669684755440,130620500241909376,-4441243727496127184,160132524268963159440,-6102784264210449418144
%N E.g.f. satisfies A(x) = exp( x * (1+x/2)/A(x) ).
%H Seiichi Manyama, <a href="/A365056/b365056.txt">Table of n, a(n) for n = 0..403</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( LambertW(x * (1+x/2)) ).
%F a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (-k+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*(1+x/2)))))
%Y Cf. A365053, A365054, A365055.
%Y Cf. A365038.
%K sign
%O 0,5
%A _Seiichi Manyama_, Aug 19 2023