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A296677
Expansion of e.g.f. arctan(arcsin(x)) (odd powers only).
2
1, -1, 13, -173, 12409, -370137, 88556037, -2668274373, 2491377242481, 34526890553679, 202383113207336829, 25792743610973373219, 39172126704113226631401, 12501799823936578879327095, 15717805122762984314778029685, 9078237580992214462785729689355
OFFSET
0,3
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}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 18 2017
STATUS
approved