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Search: id:A002430
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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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+0
10
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| 1, 1, 2, 17, 62, 1382, 21844, 929569, 6404582, 443861162, 18888466084, 113927491862, 58870668456604, 8374643517010684, 689005380505609448, 129848163681107301953, 1736640792209901647222, 418781231495293038913922
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) appears to be a multiple of A046990(n) (checked up to n=250). - R. Stephan, Mar 30 2004
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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, December 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, December 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, December 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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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).
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
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Cf. A036279 (denominators), A000182.
Sequence in context: A100518 A125200 A071402 this_sequence A037420 A034721 A107815
Adjacent sequences: A002427 A002428 A002429 this_sequence A002431 A002432 A002433
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KEYWORD
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nonn,easy,frac
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AUTHOR
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njas
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EXTENSIONS
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More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003
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