Search: id:A036279
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%I A036279
%S A036279 1,3,15,315,2835,155925,6081075,638512875,10854718875,1856156927625,
%T A036279 194896477400625,2900518163668125,3698160658676859375,1298054391195577640625,
%U A036279 263505041412702261046875,122529844256906551386796875,4043484860477916195764296875
%N A036279 Denominators in Taylor series for tan(x).
%C A036279 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%C A036279 The Taylor series for tan(x) appears to be identical to the quotient 
               of the 'look-a-likes' of the numerator and denominator, i.e. A160469(n)/
               A156769(n).
%C A036279 (End)
%D A036279 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 75 (4.3.67).
%D A036279 G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
%D A036279 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
%D A036279 A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index 
               of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford 
               and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 74.
%D A036279 H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer 
               Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 329.
%H A036279 T. D. Noe, <a href="b036279.txt">Table of n, a(n) for n=1..100</a>
%H A036279 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A036279 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 75 (4.3.67).
%H A036279 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HyperbolicTangent.html">Hyperbolic Tangent</a>
%H A036279 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Tangent.html">Tangent</a>
%F A036279 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%F A036279 a(n) = denom((-1)^(n-1)*2^(2*n)*(2^(2*n)-1)* bernoulli(2*n)/(2*n)!)
%F A036279 (End)
%e A036279 tan(x) = x + 2 x^3/3! + 16 x^5/5! + 272 x^7/7! + ... = x+1/3*x^3+2/15*x^5+17/
               315*x^7+62/2835*x^9+O(x^10).
%e A036279 The coefficients in the expansion of tan x are 0, 1, 0, 1/3, 0, 2/15, 
               0, 17/315, 0, 62/2835, 0, 1382/155925, 0, 21844/6081075, 0, 929569/
               638512875, 0, ... = A002430/A036279
%e A036279 tanh(x) = x-1/3*x^3+2/15*x^5-17/315*x^7+62/2835*x^9-1382/155925*x^11+...
%e A036279 The coefficients in the expansion of tanh x are 0, 1, 0, -1/3, 0, 2/15, 
               0, -17/315, 0, 62/2835, 0, -1382/155925, 0, 21844/6081075, 0, -929569/
               638512875, 0, 6404582/10854718875, 0, -443861162/1856156927625, ... 
               = A002430/A036279
%Y A036279 Cf. A002430, A000182.
%Y A036279 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A036279 Cf. A160469 and A156769
%Y A036279 (End)
%Y A036279 Sequence in context: A138896 A090627 A070234 this_sequence A156769 A029758 
               A103031
%Y A036279 Adjacent sequences: A036276 A036277 A036278 this_sequence A036280 A036281 
               A036282
%K A036279 nonn,easy,frac
%O A036279 1,2
%A A036279 N. J. A. Sloane (njas(AT)research.att.com).
%E A036279 I deleted the comment by Stephen Crowley. His formula leads to incorrect 
               values for higher values of this series Johannes W. Meijer (meijgia(AT)hotmail.com), 
               Jan 19 2009

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