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G.f. satisfies A(x) = 1 + x*A(x)^3 + x^3*A(x).
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%I #10 Nov 04 2023 10:12:25

%S 1,1,3,13,59,294,1549,8477,47715,274468,1606284,9533595,57247969,

%T 347169053,2123148153,13079296531,81087402683,505543820304,

%U 3167578950478,19935616736595,125971005957924,798883392476824,5083047458454395,32439034490697090

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

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k+1,k) * binomial(3*n-8*k,n-3*k)/(2*n-5*k+1).

%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k+1, k)*binomial(3*n-8*k, n-3*k)/(2*n-5*k+1));

%Y Cf. A366676, A367058, A367059, A367060, A367061, A367062.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 04 2023