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%I #21 Feb 07 2017 03:59:28
%S 1,2,1,-148,-3719,-20098,5055961,403644152,7831409041,-2707151879398,
%T -472143935754479,-22085804322342748,9362259685093715401,
%U 2995219209329323622102,274269338931958691728681,-132963342779629343323496848,-70698673853383423350187244639
%N Expansion of 2 * arccot(cos(x)).
%C Odd coefficients are zero.
%H Vincenzo Librandi, <a href="/A101923/b101923.txt">Table of n, a(n) for n = 1..250</a>
%F 2*acot(cos(x)) = Pi/2 + x^2/2! + 2*x^4/4! + x^6/6! - 148*x^8/8! - 3719*x^10/10! -...
%F 2*atan(cos(x)) = Pi/2 - x^2/2! - 2*x^4/4! - x^6/6! + 148*x^8/8! + 3719*x^10/10! +...
%F 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
%p with(gfun):
%p series(sin(x)/(1-(1/2)*sin(x)^2), x, 35):
%p L := seriestolist(%):
%p seq(op(2*i, L)*(2*i-1)!, i = 1..floor((1/2)*nops(L)));
%p # _Peter Bala_, Feb 06 2017
%t 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 *)
%Y Cf. A012494, A000364, A000464, A156138, A002439.
%Y 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).
%K sign,easy
%O 1,2
%A _Ralf Stephan_, Dec 27 2004
%E More terms from _Harvey P. Dale_, Nov 17 2014
%E Signs of the data entries corrected by _Peter Bala_, Feb 06 2017
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