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 A379209 #6 Dec 18 2024 09:26:27
%S A379209 1,2,9,53,357,2605,20041,160074,1314821,11036015,94242752,816190963,
%T A379209 7151741597,63287390223,564791911903,5077284164245,45935201005749,
%U A379209 417928249605123,3821430547469626,35098466575407095,323662850948066340,2995524340795970120
%N A379209 G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))).
%F A379209 a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(2*n,n-k)/(n+2*k+1).
%F A379209 a(n) = A190738(n)/(n+1).
%o A379209 (PARI) a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(2*n, n-k)/(n+2*k+1));
%Y A379209 Cf. A006013, A379189.
%Y A379209 Cf. A190738.
%K A379209 nonn
%O A379209 0,2
%A A379209 _Seiichi Manyama_, Dec 18 2024