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 A379193 #7 Dec 18 2024 09:28:11
%S A379193 1,3,16,113,921,8161,76362,742402,7425651,75918094,789808133,
%T A379193 8334087494,88983204682,959557630166,10435688564260,114329775220590,
%U A379193 1260613164978289,13978381013355836,155778935125738138,1743836357339342353,19599785557100463390,221094189317073465597,2502296315746442064053
%N A379193 G.f. A(x) satisfies A(x) = (1 + x*A(x))^2/(1 - x*A(x)^2).
%F A379193 a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(2*n+2*k+2,n-k)/(n+2*k+1).
%o A379193 (PARI) a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(2*n+2*k+2, n-k)/(n+2*k+1));
%Y A379193 Cf. A379194.
%K A379193 nonn
%O A379193 0,2
%A A379193 _Seiichi Manyama_, Dec 17 2024