A362481 E.g.f. satisfies A(x) = exp(x - x^3 * A(x)^3).

1, 1, 1, -5, -95, -959, -5159, 69721, 3113377, 64493857, 654012721, -13761498959, -1013114081759, -32273321679455, -492845589685175, 13357113599586121, 1410278045569310401, 61239473424756703681, 1270682827211021594977, -40402942687262364034463

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• sign

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362480, A362482.

Cf. A362430, A362472.

Programs

PARI

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

Formula

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).

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