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%I #16 Jul 18 2021 14:43:00
%S 1,7,31,127,73,2047,8191,4681,131071,524287,42799,8388607,33554431,
%T 19173961,536870911,2147483647,53353631,1108378657,137438953471,
%U 78536544841,2199023255551,8796093022207,162139963543,140737488355327,562949953421311,321685687669321
%N a(n) = Numerator([x^n] (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x).
%F a(n) = numerator([x^n] (cosh(2*sqrt(x)) - 2*cosh(sqrt(x)) + 1)/x).
%F a(n) = numerator (1/8)*cos(Pi*n)*Zeta(2*n+2)*Pi^(-2*n-2)/(-1+2^(2*n+2))*(-2+4^(-n))/Zeta(-1-2*n). - _Peter Luschny_, Jun 13 2020
%F a(n) = denominator((2*n + 1)!/(2^(2*n + 1) - 1)). - _Peter Luschny_, Jul 18 2021
%e r(n) = 1, 7/12, 31/360, 127/20160, 73/259200, 2047/239500800, 8191/43589145600, ...
%p gf := (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x: ser := series(gf, x, 40):
%p seq(numer(coeff(ser, x, n)), n=0..25);
%p # Alternative:
%p a := s -> (2*s + 1)!/(2^(2*s + 1) - 1):
%p seq(denom(a(n)), n = 0..25); # _Peter Luschny_, Jul 18 2021
%t a[s_] := ((1 - 2^(-1 - 2 s)) Pi^(-2 - 2 s) Cos[Pi s] Zeta[2 + 2 s])/(4 (1 - 2^(2 + 2 s)) Zeta[-1 - 2 s]);
%t Array[a, 26, 0] // Numerator (* _Peter Luschny_, Jun 13 2020 *)
%Y Denominators in A327986.
%Y Cf. A002675/A002677.
%K nonn,frac
%O 0,2
%A _Peter Luschny_, Oct 05 2019
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