A009400 Expansion of log(1+tanh(x)/cos(x)).

0, 1, -1, 3, -10, 65, -376, 2723, -22800, 226785, -2467456, 29857443, -397200640, 5785047905, -91090625536, 1544546456963, -28057896929280, 543833037679425, -11198060484591616, 244141035610073283, -5618437516698910720

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.825607669071161851569946... is the root of the equation cos(r) = tanh(r). - Vaclav Kotesovec, Jan 24 2015

Mathematica

Log[ 1+Tanh[ x ]/Cos[ x ] ]
CoefficientList[Series[Log[1 + Sec[x]*Tanh[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Crossrefs

Sequence in context: A352766 A206724 A306187 * A217388 A004102 A072638

Adjacent sequences: A009397 A009398 A009399 * A009401 A009402 A009403

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved