%I #9 Mar 26 2024 11:14:53
%S 1,2,11,72,525,4104,33647,285526,2486809,22103726,199697284,
%T 1828472914,16929944932,158246198836,1491210732346,14151603542612,
%U 135130396860130,1297381593071890,12516650939119421,121281286192026308,1179769340479567499
%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^2.
%F a(n) = 2 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(4*k+1,k)/(3*k+2).
%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349331.
%o (PARI) a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+1, k)/(3*k+2));
%Y Cf. A349331, A371483, A371517.
%Y Cf. A270386, A371523.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 26 2024
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