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A181993 Denominator of (4^n*(4^n-1)/2)*B_{2n}/(2n)!, B_{n} Bernoulli number. 1
1, 2, 6, 15, 630, 2835, 155925, 6081075, 1277025750, 10854718875, 1856156927625, 194896477400625, 2900518163668125, 3698160658676859375, 1298054391195577640625, 263505041412702261046875, 245059688513813102773593750, 4043484860477916195764296875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

FORMULA

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

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 *)

PROG

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

CROSSREFS

Cf. A046990.

Sequence in context: A356803 A261726 A302775 * A123475 A193341 A009711

Adjacent sequences: A181990 A181991 A181992 * A181994 A181995 A181996

KEYWORD

nonn,frac

AUTHOR

Peter Luschny, Apr 05 2012

STATUS

approved

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Last modified December 8 23:48 EST 2022. Contains 358698 sequences. (Running on oeis4.)