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%I #14 Oct 14 2023 13:59:39
%S 1,1,0,0,1,2,1,0,2,6,6,2,5,20,30,20,19,70,140,140,112,266,630,840,762,
%T 1176,2814,4620,5049,6204,12936,24156,31460,36894,63492,123552,185471,
%U 228800,338910,634920,1050686,1411410,1944800,3354780,5820256,8513804,11644490
%N G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^2.
%F G.f.: A(x) = 2*(1+x) / (1+sqrt(1-4*x^4*(1+x))).
%F a(n) = Sum_{k=0..floor(n/4)} binomial(k+1,n-4*k) * binomial(2*k,k)/(k+1).
%F a(n) = A366589(n) + A366589(n-1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(k+1, n-4*k)*binomial(2*k, k)/(k+1));
%Y Cf. A007477, A025227, A248100.
%Y Cf. A366556, A366558.
%Y Cf. A366589.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 13 2023
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