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G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^3.
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%I #8 Nov 12 2023 04:35:32

%S 1,1,5,32,237,1906,16179,142665,1294115,11998349,113194205,1083131419,

%T 10486939473,102548233212,1011333385507,10047289999536,

%U 100458873883179,1010138430187185,10208244014494347,103625607305637693,1056166710786300973

%N G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^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=3) = 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. A002294, A360100, A365150, A367240.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 12 2023