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 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

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)