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

%I #10 Mar 25 2023 08:19:12

%S 1,2,-2,-16,-10,118,304,-500,-3754,-2488,30866,83716,-135568,-1080972,

%T -792876,9090484,25788118,-39325156,-335074520,-271779024,2820643842,

%U 8348113120,-11788972644,-107836934448,-96107852032,900943403012,2778574561276,-3596374190416

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(4*k,n-k).

%F n*a(n) = 2 * ( (2*n-1)*a(n-1) - 4*(2*n-2)*a(n-2) + 6*(2*n-3)*a(n-3) - 4*(2*n-4)*a(n-4) + (2*n-5)*a(n-5) ) for n > 4.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x)^4))

%Y Cf. A085362, A110170, A162478, A359489, A359758, A360132, A361815, A361816.

%Y Cf. A361813.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 25 2023