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n-th derivative of sec(x)^tan(x) at x=0.
1

%I #5 Aug 20 2012 17:04:52

%S 1,0,0,3,0,30,90,588,5040,26520,325080,2158728,27731880,249259920,

%T 3181258080,36821629848,482278043520,6704476956480,93675256079040,

%U 1479108131816448,22566722722104960,390679249452835200,6559255213047250560,122197022127873558528

%N n-th derivative of sec(x)^tan(x) at x=0.

%C sec(x) = 1/cos(x).

%F E.g.f.: sec(x)^tan(x).

%p a:= n-> n!* coeff(series(sec(x)^tan(x), x, n+1), x, n):

%p seq (a(n), n=0..25); # _Alois P. Heinz_, Aug 20 2012

%t f[x_] := Sec[x]^Tan[x]; Table[Derivative[n] [f][0],{n,0,25}]

%Y Cf. A215586.

%K nonn

%O 0,4

%A _Michel Lagneau_, Aug 20 2012