A296678 Expansion of e.g.f. arctanh(arcsin(x)) (odd powers only).

1, 3, 53, 2303, 185033, 23756667, 4457821821, 1150764459063, 391167511473681, 169370797497060339, 91013260219635394629, 59435772666287730632559, 46362471059282707504957401, 42577231265939498962852834155, 45471686987452309473064526678925

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

E.g.f.: arctan(arcsinh(x)) (odd powers only, absolute values).

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

Example

arctanh(arcsin(x)) = x/1! + 3*x^3/3! + 53*x^5/5! + 2303*x^7/7! + 185033*x^9/9! + 23756667*x^11/11! + ...

Mathematica

nmax = 15; Table[(CoefficientList[Series[ArcTanh[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
nmax = 15; Table[(CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]]]/2 - Log[1 + I Log[I x + Sqrt[1 - x^2]]]/2, {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Crossrefs

Cf. A001818, A003716, A010050, A012258, A296465, A296467, A296677.

Sequence in context: A100444 A300420 A300683 * A227051 A300606 A301348

Adjacent sequences: A296675 A296676 A296677 * A296679 A296680 A296681

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2017

Status

approved