OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..372
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: x / LambertW(x*exp(-x)) = exp( x + LambertW(x*exp(-x)) ).
a(n) = Sum_{k=0..n} (-k+1)^(n-1) * binomial(n,k) = 2^n * A349719(n).
MATHEMATICA
nmax = 20; A[_] = 1;
Do[A[x_] = Exp[x + x/A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x*exp(-x)))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 01 2023
STATUS
approved