A012993 - OEIS

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A012993

arctanh(arctan(x)+arcsin(x))=2*x+15/3!*x^3+721/5!*x^5+84049/7!*x^7...

2, 15, 721, 84049, 18372769, 6443708601, 3315504514305, 2351891535306609, 2200048869778398657, 2623946039095984617321, 3886333930223496753553953, 6998154777889427559892675041 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,1`
	LINKS	`Table of n, a(n) for n=0..11.`
	FORMULA	`a(n) ~ (2n)! / r^(2n+1), where r = 0.5065231075617467173945074340469532744032... is the root of the equation arctan(r)+arcsin(r) = 1. - Vaclav Kotesovec, Feb 05 2015`
	MATHEMATICA	`nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + ArcTan[x]], {x, 0, 2nn+1}], x] Range[0, 2nn+1]!)[[n]], {n, 2, 2nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 )` `With[{nn=30}, Take[CoefficientList[Series[ArcTanh[ArcTan[x]+ArcSin[x]], {x, 0, nn}], x] Range[ 0, nn-1]!, {2, -1, 2}]] ( Harvey P. Dale, Sep 04 2022 *)`
	CROSSREFS	`Sequence in context: A013095 A208051 A038017 * A216331 A179432 A007542` `Adjacent sequences: A012990 A012991 A012992 * A012994 A012995 A012996`
	KEYWORD	`nonn`
	AUTHOR	`Patrick Demichel (patrick.demichel(AT)hp.com)`
	STATUS	`approved`

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Last modified March 31 05:51 EDT 2023. Contains 361634 sequences. (Running on oeis4.)