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A002430
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Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x).
(Formerly M2100 N0832)
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12
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1, 1, 2, 17, 62, 1382, 21844, 929569, 6404582, 443861162, 18888466084, 113927491862, 58870668456604, 8374643517010684, 689005380505609448, 129848163681107301953, 1736640792209901647222, 418781231495293038913922
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) appears to be a multiple of A046990(n) (checked up to n=250). - R. Stephan, Mar 30 2004
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
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).
(End)
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
a(n) = numer((-1)^(n-1)*2^(2*n)*(2^(2*n)-1)* bernoulli(2*n)/(2*n)!)
(End)
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EXAMPLE
| 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).
tanh(x) = x - 1/3*x^3 + 2/15*x^5 - 17/315*x^7 + 62/2835*x^9 - 1382/155925*x^11 + ...
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CROSSREFS
| Cf. A036279 (denominators), A000182.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Cf. A160469 and A156769
(End)
Sequence in context: A175450 A071402 A191295 * A160469 A176581 A037420
Adjacent sequences: A002427 A002428 A002429 * A002431 A002432 A002433
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KEYWORD
| nonn,easy,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003
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