A156036 Numerators in expansion of log(z^2/(cosh(z)-cos(z))) for exponents that are multiples of 4.

0, -1, 1, -691, 3617, -174611, 236364091, -3392780147, 7709321041217, -26315271553053477373, 261082718496449122051, -2530297234481911294093, 5609403368997817686249127547, -61628132164268458257532691681, 354198989901889536240773677094747, -1215233140483755572040304994079820246041491

Offset

0,4

References

V. Mangulis, Handbook of Series, Academic Press, 1965, p. 76.

Links

Table of n, a(n) for n=0..15.

Formula

log(z^2/(cosh(z)-cos(z))) = Sum_{ n >= 1 } (-1)^n*B_{2n}*(2z^2)^(2n)/((4n)!2n).

a(n) = numerator((-1)^n * zeta(4*n)/(zeta(2*n)*Pi^(2*n))). - Enrique Pérez Herrero, Jun 20 2012

Example

log(z^2/(cosh(z)-cos(z))) = -(1/360)*z^4+(1/302400)*z^8-(691/122594472000)*z^12+(3617/333456963840000)*z^16+...

Prog

(PARI) my(N=90, z='z+O('z^N), v=apply(numerator, Vec(log(z^2/(cosh(z)-cos(z))), -N))); vector(#v\4, k, v[4*k-2]) \\ Michel Marcus, Feb 03 2025

Crossrefs

Cf. A156032.

Sequence in context: A046753 A033563 A231273 * A029814 A135843 A130662

Adjacent sequences: A156033 A156034 A156035 * A156037 A156038 A156039

Keyword

sign,frac

Author

N. J. A. Sloane, Oct 31 2009

Extensions

Definition clarified by Michel Marcus, Feb 03 2025

Status

approved