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%I #17 Feb 16 2025 08:34:05
%S 1,1,2,11,63,542,5183,62211,830252,12900381,220566835,4223662522,
%T 88001471869,2007052809465,49309469989666,1306455781607975,
%U 36973887007453315,1116728635342926570,35775769695237122035,1213704083311914974899
%N E.g.f. satisfies A(x) = exp( (exp(x) - 1) * 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 * (exp(x) - 1)) / x ).
%F E.g.f.: Sum_{k>=0} (k*x + 1)^(k-1) * (exp(x) - 1)^k / k!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(exp(x)-1))/x)))
%Y Cf. A052880, A362800.
%Y Cf. A362794, A362796.
%Y Cf. A000110, A361777.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 04 2023