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%I #10 Aug 28 2023 10:52:03
%S 1,1,2,6,22,88,370,1613,7230,33117,154330,729369,3487470,16840346,
%T 82007012,402269702,1985867630,9858739759,49187798158,246506563980,
%U 1240337033398,6263601365616,31734939452116,161270637750264,821802841072422,4198348868249768
%N G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^4).
%F a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(2*n+1,n-2*k).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(2*n+1, n-2*k))/(2*n+1);
%Y Cf. A364739, A365247.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 28 2023