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G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^4).
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%I #8 Aug 27 2023 04:38:02

%S 1,1,2,3,-3,-50,-244,-714,-530,8522,63548,259473,535647,-1321437,

%T -19094684,-103022071,-322370363,-142186810,5537336460,41081448638,

%U 170484444654,332739198585,-1241023311708,-15677607031084,-83737193010368,-255608722098225,-12706843586158

%N G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^4).

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

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

%Y Cf. A000108, A106228, A127897, A364864.

%Y Cf. A365224, A365226.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 27 2023