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A012726 arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8... 0
0, 2, 16, 560, 39296, 4768768, 881315840, 230827284480, 81324940394496, 37097190468747264, 21272100905987080192, 14977571327515946909696, 12703902924309766749552640, 12776509288228175937154318336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) ~ (2*n-1)! / r^(2*n), where r = 0.772419882704426062944736631601064953563... is the root of the equation arctanh(r)*tan(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

With[{nn=30}, Flatten[{0, Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Tan[x]], {x, 0, nn}], x] Range[0, nn]!, {3, -1, 2}]}]] (* Harvey P. Dale, Aug 26 2014 *)

CROSSREFS

Sequence in context: A013136 A013004 A012679 * A013177 A060279 A012757

Adjacent sequences:  A012723 A012724 A012725 * A012727 A012728 A012729

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Definition clarified by Harvey P. Dale, Aug 26 2014

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015

STATUS

approved

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Last modified December 11 21:21 EST 2019. Contains 329937 sequences. (Running on oeis4.)