A362737 E.g.f. satisfies A(x) = exp(x^3 + x / A(x)).

1, 1, -1, 10, -27, 316, -3725, 63666, -1177687, 25196536, -607345209, 16391726110, -488872392371, 15968546353332, -566886190710853, 21733419523383946, -894910999976666415, 39390009619800983536, -1845602126785662907121, 91714859182521808208694

Offset: 0

Author

Seiichi Manyama, May 01 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362693, A362736.

Cf. A362691.

Programs

PARI

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

Formula

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

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