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%I #58 Mar 09 2024 08:14:30
%S 1,2,13,166,3265,87306,2957509,121400350,5857287937,324884241874,
%T 20370279663901,1424790170536470,109990236302275201,
%U 9289460282062082266,852049115732672006101,84345608594930495005966,8962937531710834906989313,1017655033307013508626619554
%N E.g.f. satisfies A(x) = exp(x*A(x)^2) / (1-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.: sqrt(LambertW( -2*x/(1-x)^2 ) / (-2*x)).
%F a(n) ~ sqrt(1 + 2*exp(-1) - sqrt(1 + 2*exp(-1))) * n^(n-1) / (2 * (sqrt(1 + 2*exp(-1)) - 1)^(3/2) * exp(2*n + 1/2) * (1 + exp(-1) - sqrt(1 + 2*exp(-1)))^n). - _Vaclav Kotesovec_, Mar 06 2023
%F a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n+k,n-k)/k!. - _Seiichi Manyama_, Mar 09 2024
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x/(1-x)^2)/(-2*x))))
%Y Cf. A352410, A360609.
%Y Cf. A052750, A352448.
%Y Cf. A370875.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 05 2023
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