%I A156769
%S A156769 1,3,15,315,2835,155925,6081075,638512875,10854718875,1856156927625,
%T A156769 194896477400625,49308808782358125,3698160658676859375,
%U A156769 1298054391195577640625,263505041412702261046875
%N A156769 A 'look-a-like' of the denominators in Taylor series for tan(x)
%C A156769 The first difference with sequence A036279 for the denominators in Taylor 
               series for tan(x) occurs at a(12).
%C A156769 The numerators of the two formulae for this sequence lead to A001316, 
               Gould's sequence.
%C A156769 Stephen Crowley indicated on Aug 25, 2008, that a(n) = denom(Zeta(2*n)/
               Zeta(1-2*n)) and here numer((Zeta(2*n)/Zeta(1-2*n))/(2*(-1)^(n)*(Pi)^(2*n))) 
               leads to Gould's sequence.
%C A156769 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%C A156769 This sequence appears in the Eta and Zeta triangles A160464 and A160474. 
               Its resemblance with the sequence of the denominators of the Taylor 
               series for tan(x) led to the conjecture A156769(n) = A036279(n)*A089170(n-1).
%C A156769 (End)
%F A156769 a(n) = denom(product(2/(k*(2*k+1)), k=1..n-1))
%F A156769 a(n) = denom(2^(2*n-2)/factorial(2*n-1))
%F A156769 G.f.: (1/2)*z^(1/2)*sinh(2*z^(1/2))
%p A156769 a := n ->(2*n-1)!*2^(add(i,i=convert(n-1,base,2))-2*n+2); [From Peter 
               Luschny (peter(AT)luschny.de), May 02 2009]
%Y A156769 Cf. A036279 Denominators in Taylor series for tan(x).
%Y A156769 Cf. A001316 Gould's sequence appears in the numerators.
%Y A156769 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A156769 A160464 and A160474 are the Eta and Zeta triangles.
%Y A156769 Equals abs(A117972(n))/A000265(n)
%Y A156769 Equals A036279(n)*A089170(n-1)
%Y A156769 Cf. A160469 A 'look-a-like' of the numerators in the Taylor series for 
               tan(x).
%Y A156769 (End)
%Y A156769 Sequence in context: A090627 A070234 A036279 this_sequence A029758 A103031 
               A012474
%Y A156769 Adjacent sequences: A156766 A156767 A156768 this_sequence A156770 A156771 
               A156772
%K A156769 easy,nonn
%O A156769 1,2
%A A156769 Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 15 2009