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%I #14 Aug 24 2023 07:49:50
%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).
%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.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 23 2023
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