login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012131 cosh(arcsin(tanh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-263/8!*x^8... 1
1, 1, -3, 21, -263, 4841, -99723, -199939, 501445617, -101818966319, 19731909099757, -4192563651606299, 1009030667701246697, -277080625752723191879, 86724157841631252590437, -30813037783471577493355059, 12363651257099764677344554977 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

Observe that arcsin(tanh(x)) = int {0..x} 1/cosh(t) so the generating function for this sequence is cosh( int {0..x} 1/cosh(t) ). Note the similarity to the generating function for A000364: cosh( int {0..x} 1/cos(t) ) = 1+x^2/2!+5*x^4/4!+61*x^6/6!+... - Peter Bala, Aug 24 2011.

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Cosh[ArcSin[Tanh[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Mar 08 2015 *)

CROSSREFS

Sequence in context: A232470 A251573 A265002 * A221094 A098278 A269938

Adjacent sequences:  A012128 A012129 A012130 * A012132 A012133 A012134

KEYWORD

sign

AUTHOR

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

EXTENSIONS

More terms from Harvey P. Dale, Mar 08 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 22 04:15 EST 2018. Contains 299429 sequences. (Running on oeis4.)