A362569 E.g.f. satisfies A(x) = exp(x/A(x)^(x^2)).

1, 1, 1, 1, -23, -119, -359, 6721, 78961, 450577, -7867439, -160506719, -1421049959, 23995634521, 745945175977, 9197488067041, -152057966904479, -6667968305775839, -107047941299543519, 1740437689443523777, 102311231044267813321, 2043217889363061489961

Offset: 0

Author

Seiichi Manyama, Apr 25 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..427
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A177885, A362568.

Cf. A362571.

Programs

PARI

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

Formula

E.g.f.: (x^3 / LambertW(x^3))^(1/x^2) = exp(LambertW(x^3) / x^2) = exp(x * exp(-LambertW(x^3))).

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

E.g.f.: Sum_{k>=0} (-k*x^2 + 1)^(k-1) * x^k / k!.