Search: id:A002430
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%I A002430 M2100 N0832
%S A002430 1,1,2,17,62,1382,21844,929569,6404582,443861162,18888466084,
%T A002430 113927491862,58870668456604,8374643517010684,689005380505609448,
%U A002430 129848163681107301953,1736640792209901647222,418781231495293038913922
%N A002430 Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x).
%C A002430 a(n) appears to be a multiple of A046990(n) (checked up to n=250). - 
               R. Stephan, Mar 30 2004
%C A002430 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%C A002430 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 A002430 (End)
%D A002430 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002430 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002430 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 A002430 G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
%D A002430 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
%D A002430 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 A002430 H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer 
               Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 329.
%H A002430 T. D. Noe, <a href="b002430.txt">Table of n, a(n) for n=1..100</a>
%H A002430 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 A002430 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 A002430 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HyperbolicTangent.html">Hyperbolic Tangent</a>
%H A002430 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Tangent.html">Tangent</a>
%F A002430 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%F A002430 a(n) = numer((-1)^(n-1)*2^(2*n)*(2^(2*n)-1)* bernoulli(2*n)/(2*n)!)
%F A002430 (End)
%e A002430 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 A002430 tanh(x) = x - 1/3*x^3 + 2/15*x^5 - 17/315*x^7 + 62/2835*x^9 - 1382/155925*x^11 
               + ...
%Y A002430 Cf. A036279 (denominators), A000182.
%Y A002430 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A002430 Cf. A160469 and A156769
%Y A002430 (End)
%Y A002430 Sequence in context: A100518 A125200 A071402 this_sequence A160469 A037420 
               A034721
%Y A002430 Adjacent sequences: A002427 A002428 A002429 this_sequence A002431 A002432 
               A002433
%K A002430 nonn,easy,frac
%O A002430 1,3
%A A002430 N. J. A. Sloane (njas(AT)research.att.com).
%E A002430 More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003

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