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Expansion of 1/sqrt(1 - 4*x^3/(1 - x)^2).
0

%I #14 Oct 05 2024 02:46:19

%S 1,0,0,2,4,6,14,34,72,154,346,774,1714,3822,8574,19238,43204,97254,

%T 219286,494962,1118502,2530522,5730762,12989634,29467718,66901378,

%U 151996338,345556218,786092266,1789284762,4074927962,9284968682,21166439112,48273612954,110142596298

%N Expansion of 1/sqrt(1 - 4*x^3/(1 - x)^2).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(n-k-1,n-3*k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x^3/(1-x)^2))

%o (PARI) a(n) = sum(k=0, n\3, binomial(2*k,k) * binomial(n-k-1,n-3*k));

%Y Partial sums are A098479.

%Y Cf. A025178, A110170.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Oct 04 2024