A279370 Numerators of coefficients in expansion of (cos(sqrt(x)))/(1 + cos(sqrt(x))).

1, -1, -1, -17, -31, -691, -5461, -929569, -3202291, -221930581, -4722116521, -56963745931, -14717667114151, -2093660879252671, -86125672563201181, -129848163681107301953, -868320396104950823611, -209390615747646519456961, -14129659550745551130667441

Offset: 0

Author

Clark Kimberling, Dec 12 2016

Keywords

• sign
• easy
• frac

Comments

Differs from A089171 in signs; see Formula.

Examples

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

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A089171, A279109, A279239, A276592.

Programs

Mathematica

z = 26; t = CoefficientList[Series[Cos[Sqrt[x]]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t]   (* A279370 *)
Denominator[t] (* A279109 *)

Formula

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