%I #29 Nov 10 2023 05:48:25
%S 1,2,12,152,2960,78112,2607808,105432448,5008584960,273482293760,
%T 16878251101184,1161918967060480,88277165100666880,
%U 7337286679766179840,662287143981044121600,64516370031367063175168,6746443728505612426870784,753763691778003738319519744
%N E.g.f. satisfies A(x) = exp(x + x * A(x)^2).
%H Seiichi Manyama, <a href="/A362694/b362694.txt">Table of n, a(n) for n = 0..339</a>
%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*exp(2*x)) / (2*x) ) = exp( x - LambertW(-2*x*exp(2*x))/2 ).
%F a(n) = Sum_{k=0..n} (2*k+1)^(n-1) * binomial(n,k) = 2^n * A202617(n).
%F a(n) ~ sqrt(1 + 1/LambertW(exp(-1))) * 2^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^n). - _Vaclav Kotesovec_, Nov 10 2023
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-2*x*exp(2*x))/2)))
%Y Cf. A349562, A362693, A362734, A362735.
%Y Cf. A143768, A202617.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 01 2023