This site is supported by donations to The OEIS Foundation.

 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.

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