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

0,3

Links

Table of n, a(n) for n=0..21.

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

Example

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.

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):

Crossrefs

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

Sequence in context: A012656 A012397 A012402 * A012654 A012651 A012401

Adjacent sequences: A177697 A177698 A177699 * A177701 A177702 A177703

Keyword

sign

Author

Michel Lagneau, May 11 2010

Extensions

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

Status

approved