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n-th derivative of sech(x)^tanh(x) at x=0.
1

%I #8 Aug 04 2018 06:39:53

%S 1,0,0,-3,0,30,90,-588,-5040,11400,325080,336072,-25237080,-126955920,

%T 2273150880,25210740552,-217110741120,-4985924326080,16380284725440,

%U 1066531842442752,1493617498611840,-249776526926340480,-1647997041357152640,63281386481329443072

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

%C sech(x) = 1/cosh(x).

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

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

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

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

%Y Cf. A215588.

%K sign

%O 0,4

%A _Michel Lagneau_, Aug 20 2012