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%I #8 Apr 18 2024 09:32:05
%S 1,3,30,369,5130,76626,1200816,19475829,324140886,5504511654,
%T 94998663000,1661370690546,29377608173460,524366947411668,
%U 9435112261205328,170958245619049173,3116653690408787070,57125853834377116014,1052116816793294021688
%N G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*(1 + x)*A(x) )^(1/3).
%F a(n) = Sum_{k=0..n} 9^k * binomial(4*k/3-2/3,k) * binomial(k,n-k)/(k+1).
%o (PARI) a(n) = sum(k=0, n, 9^k*binomial(4*k/3-2/3, k)*binomial(k, n-k)/(k+1));
%Y Cf. A180400, A372038.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 17 2024
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