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%I #14 May 04 2023 09:53:17
%S 1,1,2,12,72,650,6480,80906,1121512,18069264,320204160,6348340152,
%T 136915211664,3230148306216,82078412377416,2248247450065080,
%U 65771634671679360,2052879248516927232,67955959831214467584,2381716543764159438336
%N E.g.f. satisfies A(x) = 1/(1-x)^(A(x)^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 * log(1-x)) / x ) = 1/(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=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(-lambertw(x*log(1-x)))))
%Y Cf. A052813, A362798.
%Y Cf. A362794, A362799.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 04 2023