A177700 The n-th derivative of log(1+x)*tanh(x) evaluated at x = 0.

0, 0, 2, -3, 0, -10, 160, -756, 2688, -27504, 341248, -3113440, 29004800, -365574144, 5120567296, -69912541440, 1009388355584, -16301637449728, 281310403362816, -5030932957138944, 94747161802047488, -1897026741117419520

Offset: 0

Author

Michel Lagneau, May 11 2010

Keywords

• sign

Examples

			The second derivative is -(tanh(x)/(x+1)^2) + 2*((1 - tanh(x)^2)/(x+1)) - 2*log(x+1)tanh(x)(1 - tanh(x)^2). At x = 0 this sets a(2) = 0 + 2 - 0 = 2.
		

Links

• L. Comtet and M. Fiolet, Sur les dérivées successives d'une fonction implicite. C. R. Acad. Sci. Paris Ser. A 278 (1974), 249-251. MR0348055

Crossrefs

Cf. A177699, A133942 (derivatives of log(1+x)), A155585 (derivatives of tanh(x)).

Programs

Maple

n0:= 35: T:=array(1..n0): f:=x-> ln(1+x)*tanh(x):
for n from 1 to n0 do: T[n]:=D(f)(0):f:=D(f):od: print(T):

Extensions

a(0) inserted and keyword:sign added by R. J. Mathar, May 14 2010