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Expansion of log(1+sin(x))/cosh(x).
0

%I #13 Jun 22 2015 22:16:50

%S 0,1,-1,-2,4,20,-61,-296,1184,9680,-49201,-393120,2361844,26927680,

%T -191422141,-2138039424,17147588384,250712561920,-2289437638081,

%U -32881696158208,329955144475204,5885687604556800,-65643617893832221

%N Expansion of log(1+sin(x))/cosh(x).

%F a(n) ~ n! * 2^(n+2) * (cos(Pi*n/2) * log(cosh(Pi/2)) + arctan(sinh(Pi/2)) * sin(Pi*n/2)) / Pi^(n+1). - _Vaclav Kotesovec_, Jan 24 2015

%t Log[ 1+Sin[ x ] ]/Cosh[ x ]

%t CoefficientList[Series[Log[1 + Sin[x]]*Sech[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997