A361817 Expansion of 1/sqrt(1 - 4*x*(1-x)^4).

1, 2, -2, -16, -10, 118, 304, -500, -3754, -2488, 30866, 83716, -135568, -1080972, -792876, 9090484, 25788118, -39325156, -335074520, -271779024, 2820643842, 8348113120, -11788972644, -107836934448, -96107852032, 900943403012, 2778574561276, -3596374190416

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

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

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.

Prog

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

Crossrefs

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

Cf. A361813.

Sequence in context: A112327 A152541 A302339 * A093114 A016740 A353915

Adjacent sequences: A361814 A361815 A361816 * A361818 A361819 A361820

Keyword

sign

Author

Seiichi Manyama, Mar 25 2023

Status

approved