%I #15 May 04 2023 09:53:14

%S 1,1,2,6,48,360,2820,31500,393568,5111568,78491520,1345893120,

%T 24286008384,483716087712,10526811186528,241867328844960,

%U 5957816820215040,157412355684364800,4380674530640290560,128826276098289179904,4010282529115722232320

%N E.g.f. satisfies A(x) = 1/(1-x)^(A(x)^(x^2)).

%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^2 * log(1-x)) / x^2 ) = 1/(1-x)^exp( -LambertW(x^2 * log(1-x)) ).

%F E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * (-log(1-x))^k / k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(-lambertw(x^2*log(1-x)))))

%Y Cf. A052813, A362796.

%Y Cf. A362795, A362800.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 04 2023