%I #21 Dec 02 2024 09:50:32

%S 1,1,5,26,150,925,5967,39772,271758,1893431,13400897,96078789,

%T 696333585,5093266409,37549674939,278739057687,2081637677823,

%U 15628794649931,117897848681271,893167062280029,6792410218680749,51835002735642287,396821349652564273

%N G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^3.

%F If g.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n+k+1).

%F G.f.: (1/x) * Series_Reversion( x*(1 - x/(1 - x)^3) ). - _Seiichi Manyama_, Sep 24 2024

%o (PARI) a(n, s=3, t=1) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));

%Y Cf. A001003, A011270.

%Y Cf. A365151, A365152.

%Y Cf. A052529.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 23 2023