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A046976
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Numerators of Taylor series for sec(x) = 1/cos(x).
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5
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1, 1, 5, 61, 277, 50521, 540553, 199360981, 3878302429, 2404879675441, 14814847529501, 69348874393137901, 238685140977801337, 4087072509293123892361, 13181680435827682794403
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also numerator of beta(2n+1)/pi^(2n+1), where beta(m) = Sum_{k=0..inf} (-1)^k/(2k+1)^m.
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REFERENCES
| J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 384, Problem 15.
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Eric Weisstein's World of Mathematics, Secant
Eric Weisstein's World of Mathematics, Dirichlet Beta Function
Eric Weisstein's World of Mathematics, Hyperbolic Secant
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EXAMPLE
| sec(x) = 1 + 1/2*x^2 + 5/24*x^4 + 61/720*x^6 + 277/8064*x^8 + 50521/3628800*x^10 + ...
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MATHEMATICA
| Numerator[Partition[CoefficientList[Series[Sec[x], {x, 0, 30}], x], 2][[All, 1]]]
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CROSSREFS
| a(n)/A046977(n)= A000364(n)/(2n)!, cf. A053005.
Sequence in context: A142643 A201848 A087871 * A092838 A196296 A196214
Adjacent sequences: A046973 A046974 A046975 * A046977 A046978 A046979
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KEYWORD
| nonn,frac,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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