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%I #17 Apr 21 2023 05:46:02
%S 1,1,1,7,49,241,2041,26041,282913,3449377,57170161,973059121,
%T 16847893921,343341027745,7680743819113,175958943331081,
%U 4375517632543681,118932887426911681,3374685950589927649,100735118425384221025,3217474234925998764481
%N E.g.f. satisfies A(x) = exp(x + x^3 * A(x)).
%H Seiichi Manyama, <a href="/A362392/b362392.txt">Table of n, a(n) for n = 0..414</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.: exp(x - LambertW(-x^3 * exp(x))) = -LambertW(-x^3 * exp(x))/x^3.
%F a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3*exp(x)))))
%Y Column k=6 of A362378.
%Y Cf. A118395, A125500, A362393, A362430.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 20 2023
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