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%I #8 Nov 11 2023 08:45:13
%S 1,1,4,19,104,615,3829,24728,164122,1112641,7671781,53634389,
%T 379305155,2708686547,19505022538,141470864166,1032587621470,
%U 7578835132264,55901583657799,414157062713599,3080581445049863,22996511364853472,172230640045929990
%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^2)^3.
%F If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).
%o (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
%Y Cf. A001764, A367240, A367241.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 11 2023
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