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Numerator of [x^n] of the Taylor series log(arctan(x)/log(x+1)).
1

%I #13 Nov 20 2016 03:21:50

%S 1,-13,1,11,19,-10243,751,49873,2857,-72752269,434293,1524997,

%T 8181904909,-454156185199,5044289,23214243090113,5026792806787,

%U -2652186577877894731,69028763155644023

%N Numerator of [x^n] of the Taylor series log(arctan(x)/log(x+1)).

%C The inner function is arctan(x)/log(x+1) = 1 + x/2 - 5*x^2/12 - x^3/8 + 29*x^4/144 + 151*x^5/1440 - 9979*x^6/60480 - ...

%H G. C. Greubel, <a href="/A013570/b013570.txt">Table of n, a(n) for n = 1..400</a>

%e Log(arctan(x)/log(x+1)) = x/2 - 13*x^2/24 + x^3/8 + 11*x^4/192 + 19*x^5/288 - 10243*x^6/72576 + ...

%t Numerator[Take[CoefficientList[Series[Log[ArcTan[x]/Log[x + 1]], {x,0,50}], x], {1, -1, 1}]] (* _G. C. Greubel_, Nov 19 2016 *)

%K sign,frac

%O 1,2

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

%E Name edited by _R. J. Mathar_, Dec 22 2011