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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2017 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101923 Expansion of 2 * arccot(cos(x)). 3
1, 2, 1, -148, -3719, -20098, 5055961, 403644152, 7831409041, -2707151879398, -472143935754479, -22085804322342748, 9362259685093715401, 2995219209329323622102, 274269338931958691728681, -132963342779629343323496848, -70698673853383423350187244639 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Odd coefficients are zero.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..250

FORMULA

2*acot(cos(x)) = Pi/2 + x^2/2! + 2*x^4/4! + x^6/6! - 148*x^8/8! - 3719*x^10/10! -...

2*atan(cos(x)) = Pi/2 - x^2/2! - 2*x^4/4! - x^6/6! + 148*x^8/8! + 3719*x^10/10! +...

G.f. sin(x)/(1 - 1/2*sin(x)^2) = x + 2*x^3/3! + x^5/5! - 148*x^7/7! - ... - Peter Bala, Feb 06 2017

MAPLE

with(gfun):

series(sin(x)/(1-(1/2)*sin(x)^2), x, 35):

L := seriestolist(%):

seq(op(2*i, L)*(2*i-1)!, i = 1..floor((1/2)*nops(L)));

# Peter Bala, Feb 06 2017

MATHEMATICA

With[{nn=40}, Take[CoefficientList[Series[2ArcCot[Cos[x]], {x, 0, nn}], x] Range[0, nn]!, {3, -1, 2}]] (* Harvey P. Dale, Nov 17 2014 *) (* adapted by Vincenzo Librandi, Feb 07 2017 *)

CROSSREFS

Cf. A012494, A000364, A000464, A156138, A002439.

Cf. other sequences with a g.f. of the form sin(x)/(1 - k*sin^2(x)): A012494 (k=-1), A000364 (k=1), A000464 (k=2), A156138 (k=3), A002439 (k=4).

Sequence in context: A039923 A081708 A012004 * A010788 A258819 A016448

Adjacent sequences:  A101920 A101921 A101922 * A101924 A101925 A101926

KEYWORD

sign,easy

AUTHOR

Ralf Stephan, Dec 27 2004

EXTENSIONS

More terms from Harvey P. Dale, Nov 17 2014

Signs of the data entries corrected by Peter Bala, Feb 06 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 02:24 EST 2018. Contains 318036 sequences. (Running on oeis4.)