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%I #24 Jun 28 2021 06:44:56
%S 8,-4,28,-930,96012,-24144750,12602990070,-12203470904625,
%T 20180112406353900,-53495387545025175750,216267236072968468547250,
%U -1280630367874799320798794375,10743714652441927865738713818750,-124178158916511109662405449217796875
%N a(n) is the nearest integer to 8*(2*n+1)! * Bernoulli(2*n,1/2).
%C See A033473 for the numerators and A238015 for the denominators of 8*(2*n+1)!*Bernoulli(2*n,1/2).
%C As _Robert Israel_ remarks, this expression is no longer an integer for n = 15, 23, 27, 29, 30, 31, 39, 43, 45, 46, 47, ... That's why "nearest integer" has been prefixed. - _M. F. Hasler_, Feb 16 2014
%C It can be seen that the denominator of (2*n+1)! * Bernoulli(2*n,1/2) is never more than 2^log_2(n+1). This yields A238164 as an alternative way of producing an integer sequence based on (2n+1)! * Bernoulli(2*n,1/2).
%H Vincenzo Librandi, <a href="/A238163/b238163.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>
%t a[n_] := Round[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* _Robert G. Wilson v_, Feb 17 2014 *)
%o (PARI) A238163=n->round(8*(2*n+1)!*subst(bernpol(2*n,x),x,1/2)) \\ _M. F. Hasler_, Feb 16 2014
%Y Cf. A033473, A238015, A238164.
%K sign
%O 0,1
%A _M. F. Hasler_, Feb 18 2014
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