A067630 Denominators in power series for cos(x)*cosh(x).

1, 6, 2520, 7484400, 81729648000, 2375880867360000, 151476660579404160000, 18608907752179801056000000, 4015057936610313875842560000000, 1419041926536183233139035980800000000, 778117449996850714059458989711872000000000

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

cos(x)*cosh(x) = Sum_{n>=0} (-1)^n*x^(4*n)/a(n).

a(n) = (4*n)! / 4^n = A000680(2*n).

E.g.f.: 1/(1-x^4/4). - Mohammad K. Azarian, Mar 20 2012

a(n) = n!*A060706(n). - Bruno Berselli, Mar 21 2012

From Amiram Eldar, Jan 18 2021: (Start)

Sum_{n>=0} 1/a(n) = (cos(sqrt(2)) + cosh(sqrt(2)))/2.

Sum_{n>=0} (-1)^n/a(n) = cos(1)*cosh(1). (End)

D-finite with recurrence: a(n) - (64*n^4 - 96*n^3 + 44*n^2 - 6*n)*a(n-1) = 0. - Georg Fischer, Aug 17 2021

Maple

f:= gfun:-rectoproc({a(n) - (64*n^4-96*n^3+44*n^2-6*n)*a(n-1), a(0)=1}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Aug 17 2021

Mathematica

a[n_] := (4*n)!/4^n; Array[a, 10, 0] (* Amiram Eldar, Jan 18 2021 *)

Prog

(PARI) my(x='x+O('x^50), v=apply(denominator, Vec(cos(x)*cosh(x)))); vector(#v\4, k, v[4*k-3]) \\ Michel Marcus, Jan 18 2021

Crossrefs

Cf. A000680, A060706.

Sequence in context: A279533 A069643 A264801 * A181700 A199147 A097871

Adjacent sequences: A067627 A067628 A067629 * A067631 A067632 A067633

Keyword

nonn

Author

Benoit Cloitre, Feb 02 2002

Status

approved