A096725 Numerators of terms in series expansion of (sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))).

1, 5, 1313, -2773, -701933647, -86849082293, -174426488476171, -130176915706274917, -42426469007472079018663, -24495552034235134641205327, -3019410235003955483667737236843, -74265172933666226350348992663473, -2457268368880426576340457161112391, -589361165665450343618737576026916723726003

Offset

0,2

References

V. I. Arnold, Huygens and Barrow, Newton and Hooke, Birkhäuser, Basel, 1990.

Links

G. C. Greubel, Table of n, a(n) for n = 0..180

Example

(sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))) = 1 + 5/3*x^2 + 1313/1890*x^4 - 2773/11907*x^6 - 701933647/1650310200*x^8 - 86849082293/270320810760*x^10 - ...

Mathematica

Numerator[Take[CoefficientList[Series[(Sin[Tan[x]] - Tan[Sin[x]]) / (ArcSin[ArcTan[x]] - ArcTan[ArcSin[x]]), {x, 0, 50}], x], {1, -1, 2}]] (* G. C. Greubel, Nov 20 2016 *)

Crossrefs

Cf. A096730, A096722, A096717, A096718, A096664, A096671, A096712, A096716, A045688, A045689, A096719, A096720.

Sequence in context: A182345 A268485 A066162 * A332536 A172920 A062598

Adjacent sequences: A096722 A096723 A096724 * A096726 A096727 A096728

Keyword

sign,frac

Author

N. J. A. Sloane, Aug 15 2004

Status

approved