OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} 4^k * binomial(1/2,k) * binomial(n-1,n-k).
a(n) = (-1)^(n-1) * 2 * A005043(n-1) for n > 0.
a(n) ~ (-1)^(n+1) * 3^(n + 1/2) / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 16 2024
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sqrt((1+3*x)/(1-x)))
(PARI) a(n) = sum(k=0, n, 4^k*binomial(1/2, k)*binomial(n-1, n-k));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 16 2024
STATUS
approved