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%I #19 Feb 16 2025 08:34:05
%S 1,1,0,6,0,170,-120,12446,-35336,1832400,-12172320,469680552,
%T -5524990416,189586178184,-3321122831208,111608536026360,
%U -2599887499382400,90253048158627072,-2595580675897337856,95720854442948910720,-3237436187047116892800
%N E.g.f. satisfies A(x) = (1+x)^(A(x)^x).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp( -LambertW(-x * log(1+x)) / x ) = (1+x)^exp( -LambertW(-x * log(1+x)) ).
%F E.g.f.: Sum_{k>=0} (k*x + 1)^(k-1) * (log(1+x))^k / k!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x)^exp(-lambertw(-x*log(1+x)))))
%Y Cf. A033917, A362795.
%Y Cf. A362796, A362799.
%Y Cf. A349504, A349505.
%K sign,changed
%O 0,4
%A _Seiichi Manyama_, May 04 2023