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 A135863 #21 Feb 03 2023 09:05:24 %S A135863 1,4,8,8,0,-8,0,16,0,-40,0,112,0,-336,0,1056,0,-3432,0,11440,0,-38896, %T A135863 0,134368,0,-470288,0,1664096,0,-5943200,0,21395520,0,-77558760,0, %U A135863 282861360,0,-1037158320,0,3821109600,0,-14138105520,0,52512963360,0,-195730136160 %N A135863 G.f. A(x) = 1 + 4*x*A(x)^(1/2); A(x) = 1 + 8*x^2 + 4*x*sqrt(1 + 4*x^2). %F A135863 a(n) = -4^n*binomial(n/2,n)/(n/2 - 1), except a(2) = 8, for n>=0. %F A135863 G.f.: (exp(asinh(2*x)))^2. - _Philippe Deléham_, Feb 01 2012 %F A135863 D-finite with recurrence: (-n+1)*a(n) +(-n+2)*a(n-1) +4*(-n+4)*a(n-2) +4*(-n+5)*a(n-3)=0. - _R. J. Mathar_, Jan 23 2020 %F A135863 From _Alexander Burstein_, Mar 27 2022: (Start) %F A135863 G.f. satisfies: A(-x) = 1/A(x). %F A135863 a(2*n+3) = (-1)^n*8*A000108(n) for n>=0. (End) %o A135863 (PARI) a(n)=4^n*if(n==2,1/2,binomial(n/2,n)/(1-n/2)) %Y A135863 Cf. A135864, A214377, A000108. %K A135863 sign %O A135863 0,2 %A A135863 _Paul D. Hanna_, Dec 02 2007