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%I #8 Aug 25 2023 09:43:48
%S 1,1,5,32,237,1905,16160,142392,1290613,11955947,112697701,1077438356,
%T 10422562156,101827196684,1003312506776,9958506719664,99479743121349,
%U 999370184665407,10090067735619023,102330789530653912,1041997707624103589,10648963961114066129
%N G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^2).
%F a(n) = Sum_{k=0..n} binomial(2*n+2*k+1,k) * binomial(k,n-k)/(2*n+2*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(2*n+2*k+1, k)*binomial(k, n-k)/(2*n+2*k+1));
%Y Cf. A002294, A365178, A365180, A365182, A365183.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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