A089171 Numerators of series coefficients of 1/(1 + cosh(sqrt(x))).

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

Offset

0,4

Comments

Unsigned version is equal to A002425 up to n=11, but differs beyond that point.

Unsigned version: numerators of series coefficients of 1/(1 + cos(sqrt(x))); see Mathematica. - Clark Kimberling, Dec 06 2016

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..299

Formula

a(n) = numerator(c(n+1)) where c(n)=(2^(2*n)-1)*B(2*n)/(2*n)!, B(k) denotes the k-th Bernoulli number. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Numerators of expansion of cosec(x)-cot(x) = 1/2*x+1/4*x^3/3!+1/2*x^5/5!+17/8*x^7/7!+31/2*x^9/9!+... - Ralf Stephan, Dec 21 2004 (Comment was applied to wrong entry, corrected by Alessandro Musesti (musesti(AT)gmail.com), Nov 02 2007)

E.g.f.: 1/sin(x)-cot(x). - Sergei N. Gladkovskii, Nov 22 2011

E.g.f.: x/G(0); G(k)=4k+2-x^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011

E.g.f.: (1+x/(x-2*Q(0))/2; Q(k)=8k+2+x/(1+(2k+1)*(2k+2)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011

E.g.f.: x/(x+Q(0)); Q(k)=x+(x^2)/((4*k+1)*(4*k+2)-(4*k+1)*(4*k+2)/(1+(4*k+3)*(4*k+4)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011

E.g.f.: T(0)/2, where T(k) = 1 - x^2/(x^2 - (4*k+2)*(4*k+6)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 12 2013

Aerated, these are the numerators of the Taylor series coefficients of 2 * tanh(x/2) (cf. A000182 and A198631). - Tom Copeland, Oct 19 2016

Maple

with(numtheory): c := n->(2^(2*n)-1)*bernoulli(2*n)/(2*n)!; seq(numer(c(n)), n=1..20); # C. Ronaldo

Mathematica

Numerator[CoefficientList[Series[1/(1+Cosh[Sqrt[x]]), {x, 0, 24}], x]]
Numerator[CoefficientList[Series[1/(1+Cos[Sqrt[x]]), {x, 0, 30}], x]]
(* unsigned version, Clark Kimberling, Dec 06 2016 *)

Crossrefs

Cf. A002425, A050970, A002430, A046990.

Cf. A000182, A198631, A279009, A279010.

Cf. A276592, A279370.

Sequence in context: A146731 A146667 A146462 * A279370 A276592 A002425

Adjacent sequences: A089168 A089169 A089170 * A089172 A089173 A089174

Keyword

sign,frac

Author

Wouter Meeussen, Dec 07 2003

Status

approved