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A012040 arcsinh(sin(arcsinh(x)))=x-3/3!*x^3+49/5!*x^5-2075/7!*x^7+168865/9!*x^9... 1
1, -3, 49, -2075, 168865, -22606675, 4522468625, -1266169501675, 473063766306625, -227507081427747875, 136918092950286480625, -100805803028947763426875, 89129323309512937147750625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..214

FORMULA

a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = sin(arcsinh(1)) = 0.77161333407259735231..., c = 0.95768520757339211... . - Vaclav Kotesovec, Feb 03 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcSinh[Sin[ArcSinh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 03 2015 *)

CROSSREFS

Sequence in context: A012068 A012126 A203513 * A012223 A012100 A106842

Adjacent sequences:  A012037 A012038 A012039 * A012041 A012042 A012043

KEYWORD

sign

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

STATUS

approved

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)