A362568 E.g.f. satisfies A(x) = exp(x/A(x)^x).

1, 1, 1, -5, -23, 121, 1321, -7349, -148175, 853777, 27840241, -163354949, -7934320679, 46820981065, 3203091569497, -18833438286389, -1742847946697759, 10137524365568161, 1230956201929018465, -7042544858204663813, -1095864481054115534519

Offset: 0

Author

Seiichi Manyama, Apr 25 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..417
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A177885, A362569.

Cf. A361777.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(x^2)))))

Formula

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

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

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