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%I #10 Oct 17 2023 08:19:31
%S 1,3,13,106,1000,10315,112732,1282262,15021212,179994093,2195807684,
%T 27179964798,340514877488,4309512389582,55014793453124,
%U 707582318505678,9160219144520568,119268621622902920,1560830776582842660,20519083242145870778,270851956372499374728
%N G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^4.
%F a(n) = Sum_{k=0..n} binomial(2*(3*k+1),n-k) * binomial(4*k,k)/(3*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(2*(3*k+1), n-k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A366267, A366699, A366700.
%Y Cf. A364621.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 16 2023