OFFSET
0,3
FORMULA
E.g.f.: 1/(1 - x*cos(x)/(1 - x*cos(x)/(1 - x*cos(x)/(1 - x*cos(x)/(1 - ...))))), a continued fraction.
a(n) ~ sqrt(2 - 2*r*sqrt(16*r^2 - 1)) * n^(n-1) / (exp(n) * r^n), where r = A196605 = 0.2585985822541894903... is the root of the equation r*cos(r) = 1/4. - Vaclav Kotesovec, Nov 18 2017
MAPLE
a:=series(2/(1+sqrt(1-4*x*cos(x))), x=0, 21): seq(n!*coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 19; CoefficientList[Series[2/(1 + Sqrt[1 - 4 x Cos[x]]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Cos[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 18 2017
STATUS
approved