A376809 Expansion of 1/sqrt(1 - 4*x^3/(1 - x)^2).

1, 0, 0, 2, 4, 6, 14, 34, 72, 154, 346, 774, 1714, 3822, 8574, 19238, 43204, 97254, 219286, 494962, 1118502, 2530522, 5730762, 12989634, 29467718, 66901378, 151996338, 345556218, 786092266, 1789284762, 4074927962, 9284968682, 21166439112, 48273612954, 110142596298

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x^3/(1-x)^2))
(PARI) a(n) = sum(k=0, n\3, binomial(2*k, k) * binomial(n-k-1, n-3*k));

Crossrefs

Partial sums are A098479.

Cf. A025178, A110170.

Sequence in context: A058059 A053686 A080198 * A077637 A077639 A039791

Adjacent sequences: A376806 A376807 A376808 * A376810 A376811 A376812

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 04 2024

Status

approved