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E.g.f. satisfies A(x) = exp(x - x^3 * A(x)^3).
3

%I #13 Feb 16 2025 08:34:05

%S 1,1,1,-5,-95,-959,-5159,69721,3113377,64493857,654012721,

%T -13761498959,-1013114081759,-32273321679455,-492845589685175,

%U 13357113599586121,1410278045569310401,61239473424756703681,1270682827211021594977,-40402942687262364034463

%N E.g.f. satisfies A(x) = exp(x - x^3 * A(x)^3).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp(x - LambertW(3*x^3 * exp(3*x))/3) = ( LambertW(3*x^3 * exp(3*x))/(3*x^3) )^(1/3).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(3*x^3*exp(3*x))/3)))

%Y Cf. A362480, A362482.

%Y Cf. A362430, A362472.

%K sign,changed

%O 0,4

%A _Seiichi Manyama_, Apr 21 2023