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%I #8 Nov 11 2023 08:45:09
%S 1,1,5,29,192,1372,10314,80390,643774,5264984,43788393,369221844,
%T 3149085162,27119598885,235495141963,2059677411141,18127763268114,
%U 160433599528417,1426870597505859,12746368353418175,114316604199957112,1028937342955189009
%N G.f. satisfies A(x) = 1 + x*A(x)^2 / (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=2, 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, A367239, A367241.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 11 2023
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