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 A285866 #17 Mar 26 2021 12:17:25
%S A285866 1,-2,11,-6,127,-10,221,-14,367,-18,-1895,-22,1447237,-26,-57253,-30,
%T A285866 118526399,-34,-5749677193,-38,91546283957,-42,-1792042789427,-46,
%U A285866 1982765468376757,-50,-286994504449237,-54,3187598676787485443,-58,-4625594554880206360895,-62
%N A285866 a(n) = numerator((-2)^n*Sum_{k=0..n} binomial(n,k) * Bernoulli(k, 1/2)).
%C A285866 Previous name: Numerators of alternating row sums of the rational triangle B2 = A285864/A285865.
%C A285866 The denominators are given in A141459.
%F A285866 a(n) = numerator(Sum_{m=0..n} (-1)^m*A285864(n, m)/A285865(n, m)), n >= 0, where the rational triangle is B2(n, m) = binomial(m, m)*2^(n-m)*B(n-m), with the Bernoulli numbers B(k) = A027641(k)/A027642(k).
%p A285866 a := n -> numer((-2)^n*add(binomial(n,k)*bernoulli(k,1/2), k=0..n)):
%p A285866 seq(a(n), n=0..31); # _Peter Luschny_, Jul 24 2020
%t A285866 a[n_] := (-2)^n Sum[Binomial[n, k] BernoulliB[k, 1/2], {k, 0, n}] // Numerator;
%t A285866 Table[a[n], {n, 0, 31}] (* _Peter Luschny_, Jul 24 2020 *)
%o A285866 (SageMath) # uses [gen_bernoulli_number from A157811]
%o A285866 print([numerator((-1)^n*gen_bernoulli_number(n, 2)) for n in range(33)]) # _Peter Luschny_, Mar 26 2021
%Y A285866 Cf. A027641/A027642, A141459, A285864/A285865.
%Y A285866 See also A157781/A157782 and A157811/A285068.
%K A285866 sign,easy,frac
%O A285866 0,2
%A A285866 _Wolfdieter Lang_, May 03 2017
%E A285866 More terms from _Indranil Ghosh_, May 06 2017
%E A285866 New name by _Peter Luschny_, Jul 24 2020