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G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^4).
1

%I #7 Apr 11 2024 10:10:18

%S 1,1,3,8,21,61,203,724,2600,9291,33525,123537,463796,1759184,6706976,

%T 25696524,99069838,384429159,1499778661,5875513183,23099489574,

%U 91123553946,360649997698,1431724692900,5699142280127,22741352276386,90949212893978

%N G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^4).

%F a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-4*k,n-k-1) for n > 0.

%o (PARI) a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);

%Y Cf. A349331, A364748, A367724, A371890.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 11 2024