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%I #9 Jul 29 2023 10:56:10
%S 1,1,1,2,5,11,26,71,197,540,1521,4401,12826,37597,111385,332861,
%T 1000181,3021071,9174308,27987989,85712801,263438881,812394661,
%U 2512807846,7793552386,24233089051,75526196851,235897169106,738271145577,2314825565700,7270693111431
%N G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^5.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k) * binomial(5*k,k) / (4*k+1).
%o (PARI) a(n) = sum(k=0, n\3, binomial(n, 3*k)*binomial(5*k, k)/(4*k+1));
%Y Cf. A364595, A364596.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Jul 29 2023
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