OFFSET
1,2
COMMENTS
Resembles A036279, the denominators in the Taylor series for tan(x). The first difference occurs at a(12).
The numerators of the two formulas for this sequence lead to A001316, Gould's sequence.
Stephen Crowley indicated on Aug 25 2008 that a(n) = denominator(Zeta(2*n)/Zeta(1-2*n)) and here numerator((Zeta(2*n)/Zeta(1-2*n))/(2*(-1)^(n)*(Pi)^(2*n))) leads to Gould's sequence.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..250
FORMULA
a(n) = denominator( Product_{k=1..n-1} 2/(k*(2*k+1)) ).
G.f.: (1/2)*z^(1/2)*sinh(2*z^(1/2)).
From Johannes W. Meijer, May 24 2009: (Start)
a(n) = A049606(2*n-1). - Zhujun Zhang, May 29 2019
MAPLE
a := n ->(2*n-1)!*2^(add(i, i=convert(n-1, base, 2))-2*n+2); # Peter Luschny, May 02 2009
MATHEMATICA
a[n_] := Denominator[4^(n-1)/(2n-1)!];
Array[a, 15] (* Jean-François Alcover, Jun 20 2018 *)
PROG
(Magma) [Denominator(4^(n-1)/Factorial(2*n-1)): n in [1..25]]; // G. C. Greubel, Jun 19 2021
(Sage) [denominator(4^(n-1)/factorial(2*n-1)) for n in (1..25)] # G. C. Greubel, Jun 19 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Feb 15 2009
STATUS
approved