OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2023
STATUS
approved