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A036279
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Denominators in Taylor series for tan(x).
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12
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1, 3, 15, 315, 2835, 155925, 6081075, 638512875, 10854718875, 1856156927625, 194896477400625, 2900518163668125, 3698160658676859375, 1298054391195577640625, 263505041412702261046875, 122529844256906551386796875, 4043484860477916195764296875
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OFFSET
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1,2
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COMMENTS
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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). - Johannes W. Meijer, May 24 2009
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REFERENCES
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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).
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
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.
H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 329.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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).
Eric Weisstein's World of Mathematics, Hyperbolic Tangent
Eric Weisstein's World of Mathematics, Tangent
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FORMULA
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a(n) = denom((-1)^(n-1)*2^(2*n)*(2^(2*n)-1)* bernoulli(2*n)/(2*n)!). - Johannes W. Meijer, May 24 2009
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EXAMPLE
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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).
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
tanh(x) = x-1/3*x^3+2/15*x^5-17/315*x^7+62/2835*x^9-1382/155925*x^11+...
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
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CROSSREFS
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Cf. A002430, A000182.
Cf. A160469 and A156769. - Johannes W. Meijer, May 24 2009
Sequence in context: A138896 A090627 A070234 * A156769 A029758 A103031
Adjacent sequences: A036276 A036277 A036278 * A036280 A036281 A036282
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KEYWORD
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nonn,easy,frac
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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I deleted the comment by Stephen Crowley. His formula leads to incorrect values for higher values of this series. - Johannes W. Meijer, Jan 19 2009
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STATUS
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approved
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