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 A379330 #7 Dec 21 2024 11:10:19
%S A379330 1,2,10,66,500,4112,35702,322114,2990450,28382486,274151074,
%T A379330 2686200302,26634199776,266738477892,2694291026378,27416542767134,
%U A379330 280790643343716,2892142875601024,29939599990333394,311334925950172590,3250627732373638716,34063930480000774400,358149513590192454578
%N A379330 G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x*A(x)^2) * (1 - 2*x*A(x)) ).
%F A379330 a(n) = 2^n * Sum_{k=0..n} binomial(n/2+3*k/2+1/2,k) * binomial(3*n/2-k/2-1/2,n-k)/(n+3*k+1).
%o A379330 (PARI) a(n) = 2^n*sum(k=0, n, binomial(n/2+3*k/2+1/2, k)*binomial(3*n/2-k/2-1/2, n-k)/(n+3*k+1));
%Y A379330 Cf. A379329, A379331.
%K A379330 nonn
%O A379330 0,2
%A A379330 _Seiichi Manyama_, Dec 21 2024