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

%I #10 Oct 08 2023 10:50:21

%S 1,2,-7,69,-715,8351,-103735,1346247,-18035023,247520970,-3462344959,

%T 49181268701,-707502644111,10286493363184,-150913708053635,

%U 2231345941617611,-33215679733509159,497392118745778015,-7487512016559918595,113242852989349372915

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

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

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

%Y Cf. A007317, A199475, A349289, A349290, A349291, A349292, A349293, A366356, A366357, A366358.

%Y Cf. A364408, A366328, A366366.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 08 2023