A360293 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-1-k,k) * binomial(2*n-4*k,n-2*k).

1, 2, 6, 18, 58, 194, 662, 2290, 8002, 28178, 99830, 355426, 1270586, 4557682, 16396454, 59135458, 213745922, 774077986, 2808105318, 10202439858, 37118386490, 135210620194, 493082387766, 1799998114770, 6577045868866, 24052649767730, 88031695861590

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

G.f.: 1 / sqrt(1-4*x/(1+x^2)).

n*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*a(n-2) + 2*(2*n-7)*a(n-3) - (n-4)*a(n-4).

a(n) ~ (1 + sqrt(3))^(2*n) / (3^(1/4) * sqrt(Pi*n) * 2^(n - 1/2)). - Vaclav Kotesovec, Feb 02 2023

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n-1-k, k)*binomial(2*n-4*k, n-2*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x^2)))

Crossrefs

Cf. A360294, A360295.

Sequence in context: A193777 A157004 A293067 * A085139 A150041 A190790

Adjacent sequences: A360290 A360291 A360292 * A360294 A360295 A360296

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2023

Status

approved