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%I #25 Sep 17 2023 10:11:10
%S 1,0,1,1,4,9,27,78,231,715,2193,6954,21999,70840,228896,746650,
%T 2447757,8072208,26745627,89002364,297344960,996865397,3352918429,
%U 11310307593,38256171642,129718262583,440855654827,1501451066767,5123671576890,17516503865294
%N G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(k,n-2*k) * binomial(n+2*k+1,k) / (n+2*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(k, n-2*k)*binomial(n+2*k+1, k)/(n+2*k+1));
%Y Cf. A001005, A025250, A055113, A217358.
%Y Cf. A365690.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 17 2023
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