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A012746
arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...
0
1, 1, 13, 677, 54937, 6248713, 988579109, 212756765101, 60179200959793, 21632158018229009, 9619077100099258429, 5182270736688171740085, 3326876613520624630798281, 2509818428217896837411045913, 2198676694008933148388904662357, 2213672191262297018716557756353725
OFFSET
0,3
FORMULA
a(n) ~ (2*n)! / r^(2*n+1), where r = 0.932706009172514... is the root of the equation cos(r)*log((1-r)/(1+r)) = -2. - Vaclav Kotesovec, Nov 02 2013
MATHEMATICA
Table[n!*SeriesCoefficient[ArcTanh[ArcTanh[x]*Cos[x]], {x, 0, n}], {n, 1, 41, 2}] (* Vaclav Kotesovec, Nov 02 2013 *)
With[{nn=40}, Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Cos[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, May 20 2016 *)
CROSSREFS
Sequence in context: A298951 A157027 A042307 * A211094 A290166 A113093
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved