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Expansion of 1/(1 - 9*x*(1 + x))^(5/3).
2

%I #7 Oct 22 2024 08:00:23

%S 1,15,195,2340,26910,301158,3307590,35830080,384072975,4082949585,

%T 43113860361,452742067440,4732188244290,49266375442110,

%U 511157395433610,5287689996408612,54555878321808435,561579617798527185,5768783256563735265,59149668761521664040,605472238745163334116

%N Expansion of 1/(1 - 9*x*(1 + x))^(5/3).

%F a(n) = 3*((3*n+2)*a(n-1) + (3*n+4)*a(n-2))/n for n > 1.

%F a(n) = Sum_{k=0..n} (-9)^k * binomial(-5/3,k) * binomial(k,n-k).

%o (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-5/3, k)*binomial(k, n-k));

%Y Cf. A180400, A376568, A377260.

%Y Cf. A377235.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 21 2024