A367280 - OEIS

%I #10 Nov 12 2023 04:35:43

%S 1,1,5,33,251,2073,18069,163600,1523731,14504988,140499307,1380322749,

%T 13721269995,137758098052,1394840743638,14227181658075,

%U 146048314214619,1507739540085350,15643456882376418,163036276218805231,1706021256401103673

%N G.f. satisfies A(x) = 1 + x*A(x)^3 / (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=3, 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, A366176, A367232, A367238.

%Y Cf. A002293, A367242.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 12 2023