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A012830 arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7... 0
1, 4, 88, 4184, 398848, 58835456, 12993783424, 3911934210560, 1562951627091968, 793328025614454784, 501079933291827593216, 384338283691725654392832, 352458553186266111883247616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.7759352114645266952650140305350722729253... is the root of the equation sec(r)*arcsinh(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSinh[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

CROSSREFS

Sequence in context: A303153 A154137 A154136 * A281180 A296465 A012946

Adjacent sequences:  A012827 A012828 A012829 * A012831 A012832 A012833

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 3 10:25 EDT 2022. Contains 355050 sequences. (Running on oeis4.)