A361816 Expansion of 1/sqrt(1 - 4*x*(1-x)^3).

1, 2, 0, -10, -22, 12, 174, 344, -354, -3304, -5780, 9180, 65258, 99132, -226620, -1313580, -1690990, 5441340, 26681700, 28070100, -128211552, -543818824, -440381780, 2978145240, 11080939914, 6162798092, -68377892976, -225107280388, -64286124152

Offset: 0

Author

Seiichi Manyama, Mar 25 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=3 of A361834.

Cf. A085362, A110170, A162478, A359489, A359758, A360132, A361815, A361817.

Cf. A361812.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x)^3))

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(3*k,n-k).

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