OFFSET
0,3
FORMULA
E.g.f.: 1/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - x*cosh(x)/(1 - ...))))), a continued fraction.
a(n) ~ sqrt(2 + 2*r*sqrt(1-16*r^2)) * n^(n-1) / (exp(n) * r^n), where r = 0.2428073624074744554637516823... is the root of the equation 2*r*(exp(2*r)+1) = exp(r). - Vaclav Kotesovec, Nov 18 2017
MAPLE
a:=series(2/(1+sqrt(1-4*x*cosh(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 Cosh[x]]), {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Cosh[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 18 2017
STATUS
approved