OFFSET
0,2
REFERENCES
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..225 (terms 0..100 from T. D. Noe)
Eric Weisstein's World of Mathematics, Secant
Eric Weisstein's World of Mathematics, Hyperbolic Secant
FORMULA
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
EXAMPLE
sec(x) = 1 + 1/2*x^2 + 5/24*x^4 + 61/720*x^6 + 277/8064*x^8 + 50521/3628800*x^10 + ...
sech(x) = 1 - 1/2 *x^2 + 5/24 *x^4 - 61/720 *x^6 + 277/8064 *x^8 - ...
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(denom(R(2*n+1)), n=0..16); # Peter Luschny, Aug 25 2015
MATHEMATICA
Table[ EulerE[n]/n! // Denominator, {n, 0, 30, 2}] (* Jean-François Alcover, Oct 04 2012 *)
CROSSREFS
KEYWORD
nonn,frac,nice,easy
AUTHOR
STATUS
approved