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 A046976 Numerators of Taylor series for sec(x) = 1/cos(x). 6
 1, 1, 5, 61, 277, 50521, 540553, 199360981, 3878302429, 2404879675441, 14814847529501, 69348874393137901, 238685140977801337, 4087072509293123892361, 13181680435827682794403, 441543893249023104553682821, 2088463430347521052196056349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also numerator of beta(2n+1)/Pi^(2n+1), where beta(m) = Sum_{k=0..inf} (-1)^k/(2k+1)^m. 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. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..243 (terms 0..100 from T. D. Noe) X. Chen, Recursive formulas for zeta(2*k) and L(2*k-1), Coll. Math. J. 26 (5) (1995) 372-376. See numerators of D_(2k-1). Eric Weisstein's World of Mathematics, Secant Eric Weisstein's World of Mathematics, Dirichlet Beta Function Eric Weisstein's World of Mathematics, Hyperbolic Secant FORMULA a(n)/A046977(n) = A000364(n)/(2n)!. Let ZBS(z) = (HurwitzZeta(z,1/4) - HurwitzZeta(z,3/4))/(2^z-2) and R(z) = (cos(z*Pi/2)+sin(z*Pi/2))*(2^z-4^z)*ZBS(1-z)/(z-1)!. Then a(n) = numerator(R(2*n+1)) and A046977(n) = denominator(R(2*n+1)). - Peter Luschny, Aug 25 2015 EXAMPLE sec(x) = 1 + 1/2*x^2 + 5/24*x^4 + 61/720*x^6 + 277/8064*x^8 + 50521/3628800*x^10 + ... MAPLE ZBS := z -> (Zeta(0, z, 1/4) - Zeta(0, z, 3/4))/(2^z-2): R := n -> (-1)^floor(n/2)*(2^n-4^n)*ZBS(1-n)/(n-1)!: seq(numer(R(2*n+1)), n=0..16); # Peter Luschny, Aug 25 2015 MATHEMATICA Numerator[Partition[CoefficientList[Series[Sec[x], {x, 0, 30}], x], 2][[All, 1]]] CROSSREFS Cf. A000364, A046977, A053005, A099612. Sequence in context: A201848 A087871 A242194 * A092838 A196296 A196214 Adjacent sequences: A046973 A046974 A046975 * A046977 A046978 A046979 KEYWORD nonn,frac,nice,easy AUTHOR STATUS approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)