OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * ((1-x) * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( LambertW((1-x) * (exp(x) - 1)) ).
E.g.f.: A(x) = (1-x) * (exp(x) - 1)/LambertW((1-x) * (exp(x) - 1)).
MATHEMATICA
nmax = 19; A[_] = 1;
Do[A[x_] = Exp[-(((Exp[x]-1)*(x-1))/A[x])]+O[x]^(nmax+1)//Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 05 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*((1-x)*(exp(x)-1))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw((1-x)*(exp(x)-1)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-x)*(exp(x)-1)/lambertw((1-x)*(exp(x)-1))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 19 2022
STATUS
approved