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G.f. satisfies A(x) = 1/(1-x) + x*(1-x)*A(x)^4.
2

%I #9 Jul 29 2023 10:51:53

%S 1,2,8,49,365,3001,26193,238119,2230151,21368167,208459419,2063563791,

%T 20675793627,209277092776,2136720896514,21979879393677,

%U 227582114799201,2369983696546858,24806423607475896,260829829404493787,2753744691645428399

%N G.f. satisfies A(x) = 1/(1-x) + x*(1-x)*A(x)^4.

%F a(n) = Sum_{k=0..n} binomial(n+k,2*k) * binomial(4*k,k) / (3*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+k, 2*k)*binomial(4*k, k)/(3*k+1));

%Y Cf. A014137, A188687.

%Y Cf. A364594, A364596.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jul 29 2023