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%I #20 May 04 2023 09:52:42
%S 1,1,1,1,5,21,61,351,2521,13105,96041,933021,7098301,65348141,
%T 787190405,7896243811,88712631281,1269172794401,15784837036561,
%U 210688183375705,3486485630182581,51674172769168741,801474314335394701,15059801657898920231,258815184609843935305
%N E.g.f. satisfies A(x) = exp(x * A(x)^(x^2/6)).
%H Seiichi Manyama, <a href="/A362573/b362573.txt">Table of n, a(n) for n = 0..470</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.: (-6 * LambertW(-x^3/6) / x^3)^(6/x^2) = exp(-6 * LambertW(-x^3/6) / x^2) = exp(x * exp(-LambertW(-x^3/6))).
%F a(n) = n! * Sum_{k=0..floor(n/3)} ((n-2*k)/6)^k * binomial(n-2*k-1,k)/(n-2*k)!.
%F E.g.f.: Sum_{k>=0} (k*x^2/6 + 1)^(k-1) * x^k / k!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^3/6)))))
%Y Cf. A000272, A362572.
%Y Cf. A362571.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Apr 25 2023
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