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G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 + A(x)^5).
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%I #11 Apr 13 2024 14:38:24

%S 1,2,2,26,50,706,1650,24282,62370,940610,2554530,39150810,110311762,

%T 1709993346,4945525650,77314273562,228002115650,3587763069826,

%U 10741365151810,169903043416730,514833595840370,8177978884039490,25025386537586610

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

%F a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n-5*k-2,n-1) for n > 0.

%F a(n) == 2 (mod 8) for n > 0. - _Hugo Pfoertner_, Apr 13 2024

%o (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n-5*k-2, n-1))/n);

%Y Cf. A364393, A364394, A364396, A364397, A366364, A371893.

%Y Cf. A349312, A366268, A371562, A371341.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 13 2024