A362482 E.g.f. satisfies A(x) = exp(x - x^4 * A(x)^4).

1, 1, 1, 1, -23, -599, -8999, -104999, -868559, 5246641, 582598801, 21205760401, 571129277401, 11475082596121, 81837031796521, -7904119577117399, -596529385424263199, -28051840646006771999, -991870986521074646879, -21837506791918601443679

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362480, A362481.

Cf. A362431, A362473.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(4*x^4*exp(4*x))/4)))

Formula

E.g.f.: exp(x - LambertW(4*x^4 * exp(4*x))/4) = ( LambertW(4*x^4 * exp(4*x))/(4*x^4) )^(1/4).

a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).