%I #7 Feb 07 2019 11:51:14

%S 1,-1,-1,-17,-31,-691,-5461,-929569,-3202291,-221930581,-4722116521,

%T -56963745931,-14717667114151,-2093660879252671,-86125672563201181,

%U -129848163681107301953,-868320396104950823611,-209390615747646519456961,-14129659550745551130667441

%N Numerators of coefficients in expansion of (cos(sqrt(x)))/(1 + cos(sqrt(x))).

%C Differs from A089171 in signs; see Formula.

%H Clark Kimberling, <a href="/A279370/b279370.txt">Table of n, a(n) for n = 0..1000</a>

%F For odd n and for n = 0, we have a(n) = A089171(n); for positive even n, however, a(n) = -A089171(n)

%e (1/2) - (1/8)x - (1/48)x^2 - (17/5760)x^3 + ... ; 1/2, - 1/8, - 48/2, - 17/5760, ... = A279370/A279109.

%t z = 26; t = CoefficientList[Series[Cos[Sqrt[x]]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];

%t Numerator[t] (* A279370 *)

%t Denominator[t] (* A279109 *)

%Y Cf. A089171, A279109, A279239, A276592.

%K sign,easy,frac

%O 0,4

%A _Clark Kimberling_, Dec 12 2016