OFFSET
0,3
COMMENTS
sec(x) = 1/cos(x).
The sequence gives only 2n-th derivatives because (2n+1)-th derivatives are 0.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..90
FORMULA
a(n) = (2n)! * [x^(2n)] sec(x)^cosh(x).
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
MAPLE
b:= n-> n! *coeff(series(sec(x)^cosh(x), x, n+1), x, n):
a:= n-> b(2*n):
seq (a(n), n=0..20); # Alois P. Heinz, Aug 18 2012
MATHEMATICA
f[x_] := Sec[x]^Cosh[x]; Table[Derivative[2*n] [f][0], {n, 0, 17}]
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 18 2012
STATUS
approved