A362430 E.g.f. satisfies A(x) = exp(x - x^3 * A(x)).

1, 1, 1, -5, -47, -239, 121, 19321, 261409, 1449505, -20428559, -730564559, -10403326559, -10910781023, 3713153976169, 108037345645321, 1301173754543041, -22441761904964159, -1628466860540690207, -41339196023230498463, -189173461196772118079

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362396, A362431.

Cf. A362392.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^3*exp(x)))))

Formula

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

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