A379193 - OEIS

%I #7 Dec 18 2024 09:28:11

%S 1,3,16,113,921,8161,76362,742402,7425651,75918094,789808133,

%T 8334087494,88983204682,959557630166,10435688564260,114329775220590,

%U 1260613164978289,13978381013355836,155778935125738138,1743836357339342353,19599785557100463390,221094189317073465597,2502296315746442064053

%N G.f. A(x) satisfies A(x) = (1 + x*A(x))^2/(1 - x*A(x)^2).

%F 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 (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 Cf. A379194.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 17 2024