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G.f. satisfies A(x) = 1 + 2*x + 2*x^3*A(x)^3.
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%I #10 Nov 05 2023 09:01:20

%S 1,2,0,2,12,24,28,120,480,1056,2304,8448,27760,69600,191232,643104,

%T 1978560,5470080,16353792,52557312,159694848,468853760,1444300800,

%U 4549644288,13905927936,42219904512,131505807360,411672307200,1270614647808,3928681875456

%N G.f. satisfies A(x) = 1 + 2*x + 2*x^3*A(x)^3.

%F a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(2*k+1,n-3*k) * A001764(k).

%o (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(2*k+1, n-3*k)*binomial(3*k, k)/(2*k+1));

%Y Cf. A001764, A366555, A367072, A367073.

%Y Cf. A367113.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 05 2023