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%I #9 Apr 02 2024 08:53:38
%S 1,2,16,178,2300,32380,481932,7458370,118809868,1935217180,
%T 32083715344,539615356884,9184652815816,157908543871712,
%U 2738272978314500,47837620415491554,841151610003847564,14874918252400486060,264381545177102073600,4720297172922980155740
%N G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x))^2/2.
%F a(n) = (1/n) * Sum_{k=0..floor(n-1)/2} 2^(n-2*k) * binomial(n,k) * binomial(4*n-k,n-1-2*k) for n > 0.
%o (PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\2, 2^(n-2*k)*binomial(n, k)*binomial(4*n-k, n-1-2*k))/n);
%Y Cf. A068875, A100327, A219538.
%Y Cf. A371661.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 02 2024