%I #9 Oct 17 2023 08:34:31

%S 1,3,7,23,88,363,1576,7091,32768,154588,741442,3604495,17721394,

%T 87960004,440165522,2218289051,11248850578,57354875692,293860786178,

%U 1512169500356,7811933144432,40499933496818,210643657689644,1098802033533295,5747266778089846

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

%F G.f.: A(x) = 2*(1+x)^2 / (1+sqrt(1-4*x*(1+x)^2)).

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

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

%Y Cf. A025227, A366695.

%Y Cf. A086616.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 16 2023