A296677 Expansion of e.g.f. arctan(arcsin(x)) (odd powers only).

1, -1, 13, -173, 12409, -370137, 88556037, -2668274373, 2491377242481, 34526890553679, 202383113207336829, 25792743610973373219, 39172126704113226631401, 12501799823936578879327095, 15717805122762984314778029685, 9078237580992214462785729689355

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: (i/2)*log(1 - log(i*x + sqrt(1 - x^2))) - (i/2)*log(1 + log(i*x + sqrt(1 - x^2))), where i is the imaginary unit (odd powers only).

Example

arctan(arcsin(x)) = x/1! - x^3/3! + 13*x^5/5! - 173*x^7/7! + 12409*x^9/9! - 370137*x^11/11! + ...

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcTan[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
nmax = 16; Table[(CoefficientList[Series[(I/2) Log[1 - Log[I x + Sqrt[1 - x^2]]] - (I/2) Log[1 + Log[I x + Sqrt[1 - x^2]]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Crossrefs

Cf. A001818, A003705, A010050, A012194, A096719, A096720, A296465, A296467.

Sequence in context: A065544 A362859 A096719 * A295507 A109392 A297691

Adjacent sequences: A296674 A296675 A296676 * A296678 A296679 A296680

Keyword

sign

Author

Ilya Gutkovskiy, Dec 18 2017

Status

approved