A362674 E.g.f. satisfies A(x) = exp( x * exp(x^3) / A(x) ).

1, 1, -1, 4, -3, 136, -1685, 26496, -433783, 8415856, -184328649, 4515376240, -121983339731, 3605788384056, -115769790754813, 4012378854562456, -149305859447213295, 5937271828722146656, -251273782851599681297, 11276632158754470014304

Offset: 0

Author

Seiichi Manyama, Apr 29 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362673.

Programs

PARI

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

Formula

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

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