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Expansion of (1 - 9*x*(1 - 9*x)^(1/3))^(1/3).
2

%I #7 Oct 21 2024 08:57:02

%S 1,-3,0,36,351,2592,16443,91368,438858,1766124,6039765,28371951,

%T 345454146,5042653380,61953010137,648331999074,6013380216978,

%U 50966902431432,404617672580886,3082831238643525,23168405721857769,176910812101877094,1406600430681201138

%N Expansion of (1 - 9*x*(1 - 9*x)^(1/3))^(1/3).

%F a(n) = 9^n * Sum_{k=0..n} (-1)^k * binomial(1/3,k) * binomial(n-4*k/3-1,n-k).

%o (PARI) a(n) = 9^n*sum(k=0, n, (-1)^k*binomial(1/3, k)*binomial(n-4*k/3-1, n-k));

%Y Cf. A377243.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 21 2024