A009391 Expansion of log(1 + tanh(x))/cos(x).

0, 1, -1, 3, -4, 25, -61, 427, -1184, 12465, -49201, 555731, -2361844, 35135945, -191422141, 2990414715, -17147588384, 329655706465, -2289437638081, 45692713833379, -329955144475204, 7777794952988025, -65643617893832221

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Crossrefs

a(2n+1) = A009843(n), |a(2n)| = A009391(2n).

Programs

Mathematica

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

Formula

a(n) ~ n! * 2^(n+1) * (Pi + (1+(-1)^n) * log(2/(1+exp(Pi)))) / Pi^(n+1). - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Incorrect Mathematica program deleted by Harvey P. Dale, Oct 14 2022