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G.f. satisfies A(x) = 1 + x*A(x)^2 - x^2*A(x)^5.
1

%I #8 Nov 02 2023 10:39:58

%S 1,1,1,-2,-17,-57,-72,386,3007,10239,9205,-111000,-761932,-2419388,

%T -810428,36696186,223335951,638716047,-268768549,-12961722498,

%U -70517888953,-176288334833,256285732480,4745735309240,23204309443908,48765510266948,-144850760459972

%N G.f. satisfies A(x) = 1 + x*A(x)^2 - x^2*A(x)^5.

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n+k,k) * binomial(2*n,n-2*k) / (n+2*k+1).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n+k, k)*binomial(2*n, n-2*k)/(n+2*k+1));

%Y Cf. A082582, A367031.

%Y Cf. A001764.

%K sign

%O 0,4

%A _Seiichi Manyama_, Nov 02 2023