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%I #35 Aug 17 2021 19:20:08
%S 1,6,2520,7484400,81729648000,2375880867360000,151476660579404160000,
%T 18608907752179801056000000,4015057936610313875842560000000,
%U 1419041926536183233139035980800000000,778117449996850714059458989711872000000000
%N Denominators in power series for cos(x)*cosh(x).
%F cos(x)*cosh(x) = Sum_{n>=0} (-1)^n*x^(4*n)/a(n).
%F a(n) = (4*n)! / 4^n = A000680(2*n).
%F E.g.f.: 1/(1-x^4/4). - _Mohammad K. Azarian_, Mar 20 2012
%F a(n) = n!*A060706(n). - _Bruno Berselli_, Mar 21 2012
%F From _Amiram Eldar_, Jan 18 2021: (Start)
%F Sum_{n>=0} 1/a(n) = (cos(sqrt(2)) + cosh(sqrt(2)))/2.
%F Sum_{n>=0} (-1)^n/a(n) = cos(1)*cosh(1). (End)
%F 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
%p 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
%t a[n_] := (4*n)!/4^n; Array[a, 10, 0] (* _Amiram Eldar_, Jan 18 2021 *)
%o (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
%Y Cf. A000680, A060706.
%K nonn
%O 0,2
%A _Benoit Cloitre_, Feb 02 2002
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