%I #12 Aug 24 2023 07:49:38
%S 1,2,11,76,591,4938,43297,393006,3661500,34813530,336447364,
%T 3295264162,32636826276,326310118860,3289090885545,33386999310460,
%U 341000875306393,3501847259286514,36136109243651145,374513918968721080,3896634418483676797
%N G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x)) )^2.
%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).
%o (PARI) a(n, s=1, t=2) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));
%Y Cf. A001003, A365147.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 23 2023