This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A238163 #24 Jun 28 2021 06:44:56 %S A238163 8,-4,28,-930,96012,-24144750,12602990070,-12203470904625, %T A238163 20180112406353900,-53495387545025175750,216267236072968468547250, %U A238163 -1280630367874799320798794375,10743714652441927865738713818750,-124178158916511109662405449217796875 %N A238163 a(n) is the nearest integer to 8*(2*n+1)! * Bernoulli(2*n,1/2). %C A238163 See A033473 for the numerators and A238015 for the denominators of 8*(2*n+1)!*Bernoulli(2*n,1/2). %C A238163 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 A238163 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 A238163 Vincenzo Librandi, <a href="/A238163/b238163.txt">Table of n, a(n) for n = 0..100</a> %H A238163 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a> %t A238163 a[n_] := Round[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* _Robert G. Wilson v_, Feb 17 2014 *) %o A238163 (PARI) A238163=n->round(8*(2*n+1)!*subst(bernpol(2*n,x),x,1/2)) \\ _M. F. Hasler_, Feb 16 2014 %Y A238163 Cf. A033473, A238015, A238164. %K A238163 sign %O A238163 0,1 %A A238163 _M. F. Hasler_, Feb 18 2014