OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..379
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(5) * exp(5*n/4)). - Vaclav Kotesovec, Nov 19 2017
MAPLE
S:= series(2/(1 + sqrt(1 - 4*LambertW(x))), x, 31):
seq(coeff(S, x, n)*n!, n=0..30); # Robert Israel, Nov 20 2017
MATHEMATICA
nmax = 19; CoefficientList[Series[2/(1 + Sqrt[1 - 4 LambertW[x]]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; 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))))) \\ Michel Marcus, Nov 20 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 19 2017
STATUS
approved