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%I #15 Mar 29 2024 15:21:35
%S 1,2,15,134,1367,15032,173836,2083806,25660383,322666882,4125822703,
%T 53482104104,701223274308,9283066366256,123912439591104,
%U 1665895096499278,22537232138264271,306586712969384678,4191205834907493725,57548344232637695030,793311718924341065567
%N G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x))^2 )^2.
%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).
%o (PARI) a(n, r=2, s=2, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A371574.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 28 2024