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n-th derivative of sec(x)^tanh(x) at x=0.
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%I #5 Aug 20 2012 19:38:34

%S 1,0,0,3,0,-10,90,308,-1680,1560,123480,-43032,-5151960,40323920,

%T 538618080,-3880887592,-32036135040,815589894720,4367132072640,

%U -121636569852672,-35223107829120,29236492773887360,-32794445470765440,-6014518868589379072,45105535773064694400

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

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

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

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

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

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

%Y Cf. A215585.

%K sign

%O 0,4

%A _Michel Lagneau_, Aug 20 2012