OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: -LambertW(2 * log(1 - x))/2.
a(n) = Sum_{k=1..n} (2 * k)^(k-1) * |Stirling1(n,k)|.
a(n) ~ n^(n-1) / (sqrt(2) * (exp(exp(-1)/2)-1)^(n - 1/2) * exp(n - n*exp(-1)/2 - 1/2)). - Vaclav Kotesovec, Oct 04 2022
E.g.f.: Series_Reversion( 1 - exp(-x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024
MATHEMATICA
nmax = 17; A[_] = 0;
Do[A[x_] = -Log[1 - x]*Exp[2*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)); concat(0, Vec(serlaplace(-lambertw(2*log(1-x))/2)))
(PARI) a(n) = sum(k=1, n, (2*k)^(k-1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved