A364592 G.f. satisfies A(x) = 1/(1-x) + x*(1-x)*A(x)^4.
1, 2, 8, 49, 365, 3001, 26193, 238119, 2230151, 21368167, 208459419, 2063563791, 20675793627, 209277092776, 2136720896514, 21979879393677, 227582114799201, 2369983696546858, 24806423607475896, 260829829404493787, 2753744691645428399
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k, 2*k)*binomial(4*k, k)/(3*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+k,2*k) * binomial(4*k,k) / (3*k+1).