OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..354
FORMULA
E.g.f.: 1/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + ...))))), a continued fraction.
a(n) ~ 2^(2*n + 3/2) * n^(n-1) / (sqrt(3) * exp(3*n/4)). - Vaclav Kotesovec, Nov 19 2017
MAPLE
a:=series(2/(1+sqrt(1+4*LambertW(-x))), x=0, 19): seq(n!*coeff(a, x, n), n=0..18); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 18; CoefficientList[Series[2/(1 + Sqrt[1 + 4 LambertW[-x]]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[LambertW[-x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) x ='x+O('x^30); Vec(serlaplace(2/(1 +sqrt(1 +4*lambertw(-x))))) \\ G. C. Greubel, Jul 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 19 2017
STATUS
approved