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A364765 G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 - x*A(x)^5).

%I A364765 #28 Dec 25 2024 05:34:00
%S A364765 1,1,5,36,304,2808,27475,279845,2935987,31511097,344344868,3818320487,
%T A364765 42855633210,485923475563,5557803724920,64046876264292,
%U A364765 742908320701832,8667090253409215,101631581618367133,1197190915359577973,14160413911721178800
%N A364765 G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 / (1 - x*A(x)^5).
%H A364765 Seiichi Manyama, <a href="/A364765/b364765.txt">Table of n, a(n) for n = 0..909</a>
%F A364765 G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^4).
%F A364765 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(4*n+k,n-1-k) for n > 0.
%F A364765 a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(6*n-2*k,n-1-k) for n > 0.
%F A364765 a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} binomial(n,k) * binomial(5*n-k,n-1-2*k) for n > 0. - _Seiichi Manyama_, Apr 01 2024
%o A364765 (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(4*n+k, n-1-k))/n);
%Y A364765 Cf. A001006, A106228, A219537, A271469.
%Y A364765 Cf. A349331, A364747.
%Y A364765 Cf. A378952, A378954.
%K A364765 nonn
%O A364765 0,3
%A A364765 _Seiichi Manyama_, Aug 06 2023