A009398 Expansion of log(1+tanh(x)*tan(x)).

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

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A076417.

Programs

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 *)

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997