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G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^5).
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%I #10 Apr 12 2024 02:07:24

%S 1,1,4,17,80,414,2289,13199,78306,474630,2926744,18304543,115837726,

%T 740379722,4772461321,30989448116,202518745795,1330961476358,

%U 8791022012712,58325109518331,388523983047285,2597516226459845,17423367396517210,117223205014488833

%N G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^5).

%F a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n-5*k,n-k-1) for n > 0.

%o (PARI) a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(3*n-5*k, n-k-1))/n);

%Y Cf. A349332, A367725, A371913, A371914.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 12 2024