A190196 Denominators of a Taylor series expansion of 1/sqrt(cosh(x)) (even powers only).

1, 4, 96, 5760, 645120, 16588800, 30656102400, 11158821273600, 109310902272000, 3278015337332736000, 191637819720990720000, 25296192203170775040000, 2541356653499348743618560000, 3303763649549153366704128000000, 713612948302617127208091648000000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Philippe Flajolet, Xavier Gourdon, and Philippe Dumas, Mellin transforms and asymptotics: harmonic sums, Special volume on mathematical analysis of algorithms. Theoret. Comput. Sci. 144 (1995), no. 1-2, 3-58.

Example

1/sqrt(cosh(x)) = 1-(1/4)*x^2+(7/96)*x^4-(139/5760)*x^6+(5473/645120)*x^8-(51103/16588800)*x^10+...

Maple

a:= n-> denom(coeff(series(1/sqrt(cosh(x)), x, 2*n+1), x, 2*n)):
seq(a(n), n=0..19);  # Alois P. Heinz, Sep 19 2023

Mathematica

Denominator[Take[CoefficientList[Series[1/Sqrt[Cosh[x]], {x, 0, 40}], x], {1, -1, 2}]] (* Harvey P. Dale, Feb 04 2012 *)

Crossrefs

Cf. A190195.

Sequence in context: A062779 A077155 A013042 * A065140 A007106 A111637

Adjacent sequences: A190193 A190194 A190195 * A190197 A190198 A190199

Keyword

nonn,frac

Author

N. J. A. Sloane, May 05 2011

Status

approved