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 A379326 #9 Dec 21 2024 11:17:27
%S A379326 1,2,2,2,0,0,-2,2,-2,6,-10,14,-28,52,-86,158,-296,528,-966,1806,-3328,
%T A379326 6160,-11542,21590,-40418,76118,-143598,271138,-513524,974620,
%U A379326 -1851962,3525682,-6723794,12839190,-24550602,47010286,-90122848,172970032,-332352998,639260230
%N A379326 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x) * (1 + 2*x*A(x)) ).
%F A379326 G.f.: -(1+2*x) / (x*(1+2*x) - sqrt((x*(1+2*x))^2 + (1+2*x))).
%F A379326 a(n) = 2^n * Sum_{k=0..n} binomial(n/2-k/2+1/2,k) * binomial(n/2-k/2+1/2,n-k)/(n-k+1).
%o A379326 (PARI) a(n) = 2^n*sum(k=0, n, binomial(n/2-k/2+1/2, k)*binomial(n/2-k/2+1/2, n-k)/(n-k+1));
%Y A379326 Cf. A379327, A379328.
%K A379326 sign
%O A379326 0,2
%A A379326 _Seiichi Manyama_, Dec 21 2024