A009398 - OEIS

A009398

Expansion of log(1+tanh(x)*tan(x)).

0, 2, -12, 352, -16352, 1382912, -172372992, 30716649472, -7334631698432, 2270814362796032, -883463096359452672, 422158497266733678592, -243014206258719292915712, 165880670114405086398513152

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) ~ (2*n)! * (-1)^(n+1) * 2^(2*n) / (n * r^(2*n)), where r = 1.87510406871196116644530824107821416257011173353... (see A076417) is the root of the equation sin(r) = tanh(r). - Vaclav Kotesovec, Jan 24 2015

MATHEMATICA

Log[ 1+Tanh[ x ]*Tan[ x ] ] (* Even Part *)

nn = 20; Table[(CoefficientList[Series[Log[1 + Tan[x]*Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

CROSSREFS

Cf. A076417.

Sequence in context: A074257 A192892 A105231 * A009698 A012724 A012624

Adjacent sequences: A009395 A009396 A009397 * A009399 A009400 A009401

KEYWORD

sign

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

STATUS

approved