A033473 - OEIS

%I #27 Nov 21 2018 00:36:03

%S 8,-4,28,-930,96012,-24144750,12602990070,-12203470904625,

%T 20180112406353900,-53495387545025175750,216267236072968468547250,

%U -1280630367874799320798794375,10743714652441927865738713818750,-124178158916511109662405449217796875

%N Numerator of (2*n+1)!*8*Bernoulli(2*n,1/2).

%C As R. Israel remarks, the expression (2*n+1)!*8*Bernoulli(2*n,1/2) is no longer an integer for n = 15, 23, 27, 29, 30, 31, 39, 43, 45, 46, 47,... - _M. F. Hasler_, Feb 16 2014

%C Denominators are in A238015. See A238163 for the rounded values and A238164 for another maybe more interesting variant. - _M. F. Hasler_, Mar 01 2014

%H Vincenzo Librandi, <a href="/A033473/b033473.txt">Table of n, a(n) for n = 0..150</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%t a[n_] := Numerator[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* _Robert G. Wilson v_, Feb 17 2014, edited by _M. F. Hasler_, Mar 01 2014 *)

%t Table[Numerator[(2 n + 1)! 8 BernoulliB[2 n, 1/2]], {n, 0, 20}] (* _Vincenzo Librandi_, Feb 18 2014 *)

%o (PARI) A033473 = n->numerator((2*n+1)!*8*subst(bernpol(2*n,x),x,1/2)) \\ _M. F. Hasler_, Feb 16-18 2014

%Y Cf. A238163, A238164.

%K sign

%O 0,1

%A _N. J. A. Sloane_

%E Definition changed by _M. F. Hasler_, Feb 16 2014

%E Further edits by _M. F. Hasler_, Mar 01 2014