OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..365
FORMULA
E.g.f.: 1/(1 - tan(x)/(1 - tan(x)/(1 - tan(x)/(1 - tan(x)/(1 - ...))))), a continued fraction.
a(n) ~ sqrt(17/2) * n^(n-1) / (exp(n) * (arctan(1/4))^(n-1/2)). - Vaclav Kotesovec, Nov 18 2017
MAPLE
S:= series(cot(x)*(1 - sqrt(1 - 4*tan(x)))/2, x, 32):
seq(n!*coeff(S, x, n), n=0..30); # Robert Israel, Nov 18 2017
MATHEMATICA
nmax = 19; CoefficientList[Series[Cot[x] (1 - Sqrt[1 - 4 Tan[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Tan[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 18 2017
STATUS
approved