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A296678 Expansion of e.g.f. arctanh(arcsin(x)) (odd powers only). 0
1, 3, 53, 2303, 185033, 23756667, 4457821821, 1150764459063, 391167511473681, 169370797497060339, 91013260219635394629, 59435772666287730632559, 46362471059282707504957401, 42577231265939498962852834155, 45471686987452309473064526678925 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 05:56 EST 2021. Contains 349470 sequences. (Running on oeis4.)