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

%I #6 Aug 22 2023 14:15:06

%S 1,2,3,8,23,72,237,808,2830,10118,36779,135510,504935,1899494,7204238,

%T 27517766,105761937,408715018,1587169591,6190357852,24238696551,

%U 95244997612,375469654543,1484519159122,5885302251250,23389997790804,93172394487012

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

%F If g.f. satisfies A(x) = (1 + x/(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. A001006, A365119.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 22 2023