A361815 Expansion of 1/sqrt(1 - 4*x*(1-x)^2).

1, 2, 2, -2, -14, -32, -30, 64, 346, 752, 584, -2044, -9486, -19324, -11368, 66180, 271658, 514916, 192584, -2151612, -7949736, -13933280, -1779028, 69933368, 235295106, 378579404, -61171228, -2267724644, -7003832456, -10248117752, 5236354188, 73288104568

Offset

0,2

Comments

Diagonal of rational function 1/(1 - (1 - x*y) * (x + y)).

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A085362, A110170, A162478, A359489, A359758, A360132, A361816, A361817.

Cf. A137635.

Sequence in context: A063898 A074052 A350599 * A349564 A129409 A352029

Adjacent sequences: A361812 A361813 A361814 * A361816 A361817 A361818

Keyword

sign

Author

Seiichi Manyama, Mar 25 2023

Status

approved