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 A371612 #11 Mar 30 2024 02:36:44
%S A371612 1,2,3,12,49,218,1037,5106,25909,134410,709691,3801498,20606654,
%T A371612 112828202,623087675,3466539248,19411070496,109313442562,618713495451,
%U A371612 3517737628368,20081523836403,115058714898196,661432784830204,3813891082337178,22052422636145522
%N A371612 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2) )^2.
%F A371612 a(n) = Sum_{k=0..n} binomial(4*(n-k)+2,k) * binomial(n-1,n-k)/(2*(n-k)+1).
%o A371612 (PARI) a(n, r=2, s=1, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y A371612 Cf. A365118, A371613.
%Y A371612 Cf. A364743, A371607.
%K A371612 nonn
%O A371612 0,2
%A A371612 _Seiichi Manyama_, Mar 29 2024