A186251 2n-th derivative of sec(x)^cosh(x) at x=0.

1, 1, 11, 196, 6621, 331816, 23484911, 2215289896, 268265691081, 40520069205136, 7462406090362331, 1645244324233761736, 427705624174427756061, 129446242864616486729896, 45117167155416556090204871, 17939982317115194446562110816, 8071743191485825080634857996561

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

Sequence in context: A345342 A218818 A243646 * A234628 A105124 A272500

Adjacent sequences: A186248 A186249 A186250 * A186252 A186253 A186254

Keyword

nonn

Author

Michel Lagneau, Aug 18 2012

Status

approved