A181993 - OEIS

%I #28 Jun 18 2019 06:15:48

%S 1,2,6,15,630,2835,155925,6081075,1277025750,10854718875,

%T 1856156927625,194896477400625,2900518163668125,3698160658676859375,

%U 1298054391195577640625,263505041412702261046875,245059688513813102773593750,4043484860477916195764296875

%N Denominator of (4^n*(4^n-1)/2)*B_{2n}/(2n)!, B_{n} Bernoulli number.

%C Numerator is (-1)^(n+1)*A046990(n).

%H Michel Marcus, <a href="/A181993/b181993.txt">Table of n, a(n) for n = 0..100</a>

%H William Rowan Hamilton, <a href="https://doi.org/10.1080/14786444308644751">On an expression for the numbers of Bernoulli, by means of a definite integral, and on some connected processes of summation and integration</a>, Philosophical Magazine, 23 (1843), pp. 360-367.

%F a(n) = denominator of (1/Pi)*Integral(x>=0, (sin(x)/x)^(2*n)*sin(2*n*x)*tan(x)).

%p A181993 := n -> denom((4^n*(4^n-1)/2)*bernoulli(2*n)/(2*n)!);

%p seq(A181993(i), i=0..18);

%t a[n_] := Denominator[4^n (4^n-1)/2 BernoulliB[2n]/(2n)!];

%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Jun 18 2019 *)

%o (PARI) a(n) = denominator((4^n*(4^n-1)/2)*bernfrac(2*n)/(2*n)!); \\ _Michel Marcus_, Jun 18 2019

%Y Cf. A046990.

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Apr 05 2012