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 A371891 #7 Apr 11 2024 10:10:18
%S A371891 1,1,3,8,21,61,203,724,2600,9291,33525,123537,463796,1759184,6706976,
%T A371891 25696524,99069838,384429159,1499778661,5875513183,23099489574,
%U A371891 91123553946,360649997698,1431724692900,5699142280127,22741352276386,90949212893978
%N A371891 G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^4).
%F A371891 a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-4*k,n-k-1) for n > 0.
%o A371891 (PARI) a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);
%Y A371891 Cf. A349331, A364748, A367724, A371890.
%K A371891 nonn
%O A371891 0,3
%A A371891 _Seiichi Manyama_, Apr 11 2024