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%I #14 Jun 22 2015 22:29:49
%S 0,2,-24,742,-46424,4924442,-795624324,182148217942,-56122289514224,
%T 22395847873848242,-11236967462922272124,6923916000862956967342,
%U -5139905036702596261514024,4524378924970721231979687242
%N Expansion of log(1+tanh(x)*sin(x)).
%F a(n) ~ (2*n)! * (-1)^(n+1) / (n * r^(2*n)), where r = 0.82560766907116185156994603327818731... is the root of the equation cos(r) = tanh(r). - _Vaclav Kotesovec_, Jan 23 2015
%t Log[ 1+Tanh[ x ]*Sin[ x ] ] (* Even Part *)
%t nn = 20; Table[(CoefficientList[Series[Log[1 + Sin[x]*Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Jan 23 2015 *)
%K sign
%O 0,2
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997