|
%I #8 Nov 11 2023 08:45:02
%S 1,1,2,9,40,202,1068,5884,33356,193365,1140940,6829601,41372238,
%T 253156085,1562416632,9714660195,60795387840,382639224327,
%U 2420498032350,15380899180204,98134455984896,628425763698123,4037685422823604,26021345223509038,168164609160791154
%N G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^2.
%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=2, t=0, 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. A364742.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 11 2023
|
