A009319 - OEIS

%I #14 Jun 21 2015 21:48:48

%S 0,1,-2,4,-17,93,-649,5381,-51778,565957,-6930141,93992413,

%T -1399244076,22689478823,-398164266655,7519118564551,-152058873978384,

%U 3278894568674073,-75103386737309385,1821102601528126265

%N Expansion of log(1+log(1+x)*cos(x)).

%F a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.7426973079865501887067225087448265047287233394318... is the root of the equation exp(1/cos(r))*(r-1) = -1. - _Vaclav Kotesovec_, Jan 24 2015

%t Log[ 1+Log[ 1+x ]*Cos[ x ] ]

%t CoefficientList[Series[Log[1 + Cos[x]*Log[1 + 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 Gérard_, Mar 15 1997