OFFSET
0,2
FORMULA
G.f.: A(x) = (1-x)/(-2*x + sqrt(1-2*x+5*x^2)).
a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(n-1,n-k)/(k+1).
a(n) = 2 * A371888(n) for n > 0.
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-x)/(-2*x+sqrt(1-2*x+5*x^2)))
(PARI) a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(n-1, n-k)/(k+1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 16 2024
STATUS
approved