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%I #9 Aug 27 2023 04:39:37
%S 1,1,3,10,30,56,-167,-2813,-21515,-126135,-601812,-2179039,-3455504,
%T 32238155,430944400,3334419890,20083350422,97094186751,338485665435,
%U 274332822425,-8491831747320,-97735154210032,-732963337489636,-4341176221239330
%N G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^5).
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*n-k+1,k) * binomial(n-1,n-k)/(5*n-k+1).
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*n-k+1, k)*binomial(n-1, n-k)/(5*n-k+1));
%Y Cf. A001764, A219537, A317133, A364758, A364865.
%Y Cf. A365223, A365226.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 27 2023
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