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 A160143 #16 Mar 18 2021 06:56:40 %S A160143 1,3,25,427,12465,555731,35135945,2990414715,329655706465, %T A160143 45692713833379,1111113564712575,1595024111042171723, %U A160143 387863354088927172625,110350957750914345093747 %N A160143 a(n) = Numerator((-1)^n*Euler(2*n)*(2*n+1)/(4^(2*n+1)-2^(2*n+1))), where Euler(n) = A122045(n). %C A160143 Resembles the coefficients of the series for x/cos(x). %C A160143 The first difference with sequence A009843 (expansion of x/cos(x)) occurs at a(10). An explanation can be found in the similarity of the numerators of (2*n+1)/(2^(2*n+1)-1) and the odd numbers 2n+1 (cf. A160144). %C A160143 Similarly, A156769 resembles A036279 (from the expansion of tan(x)). %p A160143 a := n -> (-1)^iquo(n,2)*euler(n)*(n+1)/(4^(n+1)-2^(n+1)); %p A160143 seq(numer(a(2*n)),n=0..13); %Y A160143 Cf. A009843, A122045, A160144, A160145, A036279, A156769. %K A160143 frac,nonn %O A160143 0,2 %A A160143 _Peter Luschny_, May 03 2009