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%I #23 Jan 27 2017 11:05:29
%S 1,2,24,720,8064,3628800,95800320,87178291200,4184557977600,
%T 6402373705728000,97316080327065600,1124000727777607680000,
%U 9545360026665222144000,403291461126605635584000000,3209350995912777478963200000,265252859812191058636308480000000
%N Denominators of Taylor series for sec(x). Also denominators of Taylor series for sech(x) = 1/cosh(x).
%D G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
%H Seiichi Manyama, <a href="/A046977/b046977.txt">Table of n, a(n) for n = 0..225</a> (terms 0..100 from T. D. Noe)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Secant.html">Secant</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicSecant.html">Hyperbolic Secant</a>
%F A046976(n)/a(n)= A000364(n)/(2n)!.
%F 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) = denominator(R(2*n+1)) and A046976(n) = numerator(R(2*n+1)). - _Peter Luschny_, Aug 25 2015
%e sec(x) = 1 + 1/2*x^2 + 5/24*x^4 + 61/720*x^6 + 277/8064*x^8 + 50521/3628800*x^10 + ...
%e sech(x) = 1 - 1/2 *x^2 + 5/24 *x^4 - 61/720 *x^6 + 277/8064 *x^8 - ...
%p ZBS := z -> (Zeta(0,z,1/4) - Zeta(0,z,3/4))/(2^z-2):
%p R := n -> (-1)^floor(n/2)*(2^n-4^n)*ZBS(1-n)/(n-1)!:
%p seq(denom(R(2*n+1)), n=0..16); # _Peter Luschny_, Aug 25 2015
%t Table[ EulerE[n]/n! // Denominator, {n, 0, 30, 2}] (* _Jean-François Alcover_, Oct 04 2012 *)
%Y Cf. A000364, A046976, A099612.
%K nonn,frac,nice,easy
%O 0,2
%A _N. J. A. Sloane_
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