The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A012849

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A012849

arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...
(history; published version)

#8 by Vaclav Kotesovec at Thu Feb 05 15:41:12 EST 2015

STATUS

editing

approved

#7 by Vaclav Kotesovec at Thu Feb 05 15:40:39 EST 2015

FORMULA

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6588155299144662008044917663989656738607... is the root of the equation sec(r)*arctanh(r) = 1. - Vaclav Kotesovec, Feb 05 2015

STATUS

approved

editing

#6 by Harvey P. Dale at Fri Jan 03 19:07:34 EST 2014

STATUS

editing

approved

#5 by Harvey P. Dale at Fri Jan 03 19:07:27 EST 2014

NAME

arctanh(sec(x)*atanharctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[ArcTanh[Sec[x]ArcTanh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jan 03 2014 *)

EXTENSIONS

Definition clarified by Harvey P. Dale, Jan 03 2014

STATUS

approved

editing

#4 by Charles R Greathouse IV at Fri Feb 24 12:51:10 EST 2012

AUTHOR

Patrick Demichel (dmlpatrick.demichel(AT)hpfrcu03.france.hp.com)

Discussion

Fri Feb 24

12:51

OEIS Server: https://oeis.org/edit/global/108

#3 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

KEYWORD

nonn,new

nonn

AUTHOR

Patrick Demichel (dml@(AT)hpfrcu03.france.hp.com)

#2 by N. J. A. Sloane at Sun Jun 14 03:00:00 EDT 1998

REFERENCES

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Wed Dec 11 03:00:00 EST 1996

NAME

arctanh(sec(x)*atanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...

DATA

1, 7, 193, 13319, 1721281, 357281351, 108706678273, 45591739883975, 25211971076762753, 17775279702237604231, 15562493015528998511681, 16565188691481564795512967, 21067308092979783990029042241

OFFSET

0,2

REFERENCES

KEYWORD

nonn

AUTHOR

Patrick Demichel (dml@hpfrcu03.france.hp.com)

STATUS

approved