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%I #15 Aug 22 2014 16:04:06
%S 1,1,11,196,6621,331816,23484911,2215289896,268265691081,
%T 40520069205136,7462406090362331,1645244324233761736,
%U 427705624174427756061,129446242864616486729896,45117167155416556090204871,17939982317115194446562110816,8071743191485825080634857996561
%N 2n-th derivative of sec(x)^cosh(x) at x=0.
%C sec(x) = 1/cos(x).
%C The sequence gives only 2n-th derivatives because (2n+1)-th derivatives are 0.
%H Alois P. Heinz, <a href="/A186251/b186251.txt">Table of n, a(n) for n = 0..90</a>
%F a(n) = (2n)! * [x^(2n)] sec(x)^cosh(x).
%F a(n) ~ 2^(4*n+2*cosh(Pi/2)+1) * n^(2*n+cosh(Pi/2)-1/2) / (GAMMA(cosh(Pi/2)) * exp(2*n) * Pi^(2*n+cosh(Pi/2)-1/2)). - _Vaclav Kotesovec_, Aug 22 2014
%p b:= n-> n! *coeff(series(sec(x)^cosh(x), x, n+1), x, n):
%p a:= n-> b(2*n):
%p seq (a(n), n=0..20); # _Alois P. Heinz_, Aug 18 2012
%t f[x_] := Sec[x]^Cosh[x]; Table[Derivative[2*n] [f][0],{n,0,17}]
%t nmax=40; Table[(CoefficientList[Series[Sec[x]^Cosh[x],{x,0,nmax}],x] *Range[0,nmax]!)[[n]],{n,1,nmax,2}] (* _Vaclav Kotesovec_, Aug 22 2014 *)
%K nonn
%O 0,3
%A _Michel Lagneau_, Aug 18 2012