The On-Line Encyclopedia of Integer Sequences (OEIS)

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A013047

tan(sinh(x)+tan(x))=2*x+19/3!*x^3+769/5!*x^5+67345/7!*x^7...
(history; published version)

#9 by Vaclav Kotesovec at Sat Feb 07 05:55:19 EST 2015

STATUS

editing

approved

#8 by Vaclav Kotesovec at Sat Feb 07 05:55:09 EST 2015

LINKS

Vaclav Kotesovec, <a href="/A013047/b013047.txt">Table of n, a(n) for n = 0..200</a>

#7 by Vaclav Kotesovec at Sat Feb 07 05:53:49 EST 2015

FORMULA

a(n) ~ 2 * (2*n+1)! / ((cosh(r) + 1/(cos(r))^2) * r^(2*n+2)), where r = 0.6897918664614192227814262662202471295055814443118279957952... is the root of the equation sinh(r) + tan(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

#6 by Vaclav Kotesovec at Sat Feb 07 05:49:02 EST 2015

LINKS

Vaclav Kotesovec, <a href="/A013047/a013047.jpg">Graph - abs(e.g.f.) in the complex plane</a>

#5 by Vaclav Kotesovec at Sat Feb 07 05:47:08 EST 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Tan[Sinh[x] + Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

STATUS

approved

editing

#4 by Charles R Greathouse IV at Fri Feb 24 12:51:17 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

tan(sinh(x)+tan(x))=2*x+19/3!*x^3+769/5!*x^5+67345/7!*x^7...

DATA

2, 19, 769, 67345, 10170577, 2350029977, 770367837321, 339987628582481, 194352713896710433, 139694411950654484905, 123308135456808383622937, 131131181574217458549045281, 165356414397352918016200574961

OFFSET

0,1

REFERENCES

KEYWORD

nonn

AUTHOR

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

STATUS

approved