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 A326582 #10 Jul 16 2019 04:09:43 %S A326582 1,1,1,4,1,9,1,16,27,25,1,36,1,49,-75,64,1,81,-1,100,49,121,-1,144, %T A326582 125,169,-243,196,1,225,-1,256,363,289,-1225,324,1,361,-169,400,1,441, %U A326582 -1,484,135,529,-1,576,343,625,-867,676,1,729,-3025,784,361,841,-1 %N A326582 A signed variant of A309132. %C A326582 See A309132 for background and conjectures. %F A326582 a(n) = numerator(R(n+1)/4^mod(n,2)) with R(n) = n/(nB(n) + dB(n)/n) and nB(n) = numerator(B(n-1, 1/2)), dB(n) = denominator(B(n-1, 1/2)) where B(n, x) denotes the Bernoulli polynomials. %F A326582 |a(2*n)| = A309132(2*n + 1) for n >= 0. %F A326582 a(2*n+1) = (n + 1)^2 for n >= 0. %p A326582 nB := n -> numer(bernoulli(n-1,1/2)): dB := n -> denom(bernoulli(n-1,1/2)): %p A326582 R := n -> n/(nB(n) + dB(n)/n): a := n -> numer(R(n+1)/4^irem(n,2)): %p A326582 seq(a(n), n=0..58); %Y A326582 Cf. A309132, A157779, A157780. %K A326582 sign %O A326582 0,4 %A A326582 _Peter Luschny_, Jul 15 2019