%I #13 Jun 21 2015 21:48:29
%S 0,1,-2,4,-17,113,-829,6921,-68018,766909,-9668901,134950693,
%T -2070353196,34628733267,-626969184451,12218295424331,
%U -255041910240464,5677409949583369,-134260064803417113,3361378755164561417
%N Expansion of log(1+log(1+x)/cosh(x)).
%F a(n) ~ (n-1)! * (-1)^(n+1) / (1-exp(-r))^n, where r = 1.2699247771697243287665144498039831430030774... is the root of the equation 1 + exp(-2 + 2*exp(-r)) - 2*exp(exp(-r)-1)*r = 0. - _Vaclav Kotesovec_, Jan 24 2015
%t Log[ 1+Log[ 1+x ]/Cosh[ x ] ]
%t CoefficientList[Series[Log[1 + Log[1 + x]*Sech[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997