A181993 Denominator of (4^n*(4^n-1)/2)*B_{2n}/(2n)!, B_{n} Bernoulli number.

1, 2, 6, 15, 630, 2835, 155925, 6081075, 1277025750, 10854718875, 1856156927625, 194896477400625, 2900518163668125, 3698160658676859375, 1298054391195577640625, 263505041412702261046875, 245059688513813102773593750, 4043484860477916195764296875

Offset: 0

Author

Peter Luschny, Apr 05 2012

Keywords

• nonn
• frac

Comments

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

Links

• Michel Marcus, Table of n, a(n) for n = 0..100
• William Rowan Hamilton, On an expression for the numbers of Bernoulli, by means of a definite integral, and on some connected processes of summation and integration, Philosophical Magazine, 23 (1843), pp. 360-367.

Crossrefs

Cf. A046990.

Programs

Maple

A181993 := n -> denom((4^n*(4^n-1)/2)*bernoulli(2*n)/(2*n)!);
seq(A181993(i), i=0..18);

Mathematica

a[n_] := Denominator[4^n (4^n-1)/2 BernoulliB[2n]/(2n)!];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jun 18 2019 *)

PARI

a(n) = denominator((4^n*(4^n-1)/2)*bernfrac(2*n)/(2*n)!); \\ Michel Marcus, Jun 18 2019

Formula

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