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G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^4*A(x)^5).
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%I #12 Sep 18 2023 08:59:32

%S 1,1,1,1,1,2,8,29,85,211,469,1003,2263,5734,15926,45188,124730,330583,

%T 850783,2175406,5650746,15064128,41006034,112492472,307511726,

%U 833907512,2247908392,6056190352,16390505332,44659671982,122380777306,336326321179,924529751087

%N G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^4*A(x)^5).

%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k,k) * binomial(n+k+1,n-4*k) / (n+k+1) = Sum_{k=0..floor(n/5)} binomial(n+k,6*k) * binomial(6*k,k) / (5*k+1).

%o (PARI) a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(n+k+1, n-4*k)/(n+k+1));

%Y Cf. A364472, A364523, A365759, A365761.

%Y Cf. A365758.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Sep 18 2023