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%I #7 Nov 11 2023 08:45:40
%S 1,1,6,39,284,2223,18267,155445,1358073,12111306,109802183,1009001571,
%T 9376972698,87978198364,832223905371,7928413841673,76002832317437,
%U 732578811761670,7095717550127526,69029297500888522,674181392461483212,6607910786529613248
%N G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^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=3, u=1) = 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. A161797, A365113, A365150.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 11 2023
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